Properties

Label 9408.2.a
Level $9408$
Weight $2$
Character orbit 9408.a
Rep. character $\chi_{9408}(1,\cdot)$
Character field $\Q$
Dimension $164$
Newform subspaces $118$
Sturm bound $3584$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9408.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 118 \)
Sturm bound: \(3584\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9408))\).

Total New Old
Modular forms 1888 164 1724
Cusp forms 1697 164 1533
Eisenstein series 191 0 191

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(21\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(24\)
Plus space\(+\)\(77\)
Minus space\(-\)\(87\)

Trace form

\( 164 q + 164 q^{9} + O(q^{10}) \) \( 164 q + 164 q^{9} - 8 q^{13} - 8 q^{17} + 156 q^{25} + 16 q^{29} + 8 q^{37} - 8 q^{41} + 16 q^{53} - 24 q^{61} - 16 q^{69} + 8 q^{73} + 164 q^{81} - 64 q^{85} + 8 q^{89} - 8 q^{93} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9408))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7
9408.2.a.a $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $-$ $+$ $-$ \(q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots\)
9408.2.a.b $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $-$ $+$ $-$ \(q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots\)
9408.2.a.c $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $+$ $+$ $-$ \(q-q^{3}-4q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9408.2.a.d $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) $+$ $+$ $+$ \(q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.e $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) $-$ $+$ $+$ \(q-q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots\)
9408.2.a.f $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $+$ \(q-q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\)
9408.2.a.g $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9408.2.a.h $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.i $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots\)
9408.2.a.j $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.k $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
9408.2.a.l $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
9408.2.a.m $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.n $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ \(q-q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9408.2.a.o $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ \(q-q^{3}-q^{5}+q^{9}+q^{11}+q^{15}-8q^{17}+\cdots\)
9408.2.a.p $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $-$ \(q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.q $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ \(q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{15}-4q^{17}+\cdots\)
9408.2.a.r $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ \(q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots\)
9408.2.a.s $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ \(q-q^{3}+q^{9}-2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.t $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ \(q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.u $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ \(q-q^{3}+q^{9}-4q^{13}+4q^{17}+4q^{19}+\cdots\)
9408.2.a.v $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ \(q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots\)
9408.2.a.w $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ \(q-q^{3}+q^{9}+2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.x $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ \(q-q^{3}+q^{9}+2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.y $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ \(q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.z $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ \(q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{15}+4q^{17}+\cdots\)
9408.2.a.ba $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $+$ \(q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.bb $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ \(q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots\)
9408.2.a.bc $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9408.2.a.bd $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
9408.2.a.be $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots\)
9408.2.a.bf $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
9408.2.a.bg $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $+$ \(q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
9408.2.a.bh $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bi $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $+$ \(q-q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
9408.2.a.bj $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.bk $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ \(q-q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\)
9408.2.a.bl $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ \(q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
9408.2.a.bm $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ \(q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.bn $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(4\) \(0\) $+$ $+$ $-$ \(q-q^{3}+4q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9408.2.a.bo $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(4\) \(0\) $+$ $+$ $-$ \(q-q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
9408.2.a.bp $1$ $75.123$ \(\Q\) None \(0\) \(-1\) \(4\) \(0\) $-$ $+$ $+$ \(q-q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots\)
9408.2.a.bq $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-4\) \(0\) $+$ $-$ $-$ \(q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9408.2.a.br $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-4\) \(0\) $+$ $-$ $-$ \(q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
9408.2.a.bs $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-4\) \(0\) $-$ $-$ $-$ \(q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots\)
9408.2.a.bt $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $-$ $-$ $+$ \(q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
9408.2.a.bu $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $-$ $-$ $+$ \(q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.bv $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.bw $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9408.2.a.bx $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
9408.2.a.by $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bz $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
9408.2.a.ca $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
9408.2.a.cb $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9408.2.a.cc $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.cd $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $+$ \(q+q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\)
9408.2.a.ce $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ \(q+q^{3}-q^{5}+q^{9}-5q^{11}-q^{15}-4q^{17}+\cdots\)
9408.2.a.cf $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ \(q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.cg $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ \(q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots\)
9408.2.a.ch $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ \(q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.ci $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ \(q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.cj $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ \(q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.ck $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ \(q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots\)
9408.2.a.cl $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ \(q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots\)
9408.2.a.cm $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ \(q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.cn $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ \(q+q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.co $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ \(q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots\)
9408.2.a.cp $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ \(q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots\)
9408.2.a.cq $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ \(q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.cr $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ \(q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots\)
9408.2.a.cs $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\)
9408.2.a.ct $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.cu $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
9408.2.a.cv $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $+$ \(q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots\)
9408.2.a.cw $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.cx $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $+$ \(q+q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots\)
9408.2.a.cy $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
9408.2.a.cz $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
9408.2.a.da $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ \(q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
9408.2.a.db $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $+$ $-$ $-$ \(q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.dc $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $-$ $-$ $-$ \(q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
9408.2.a.dd $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(4\) \(0\) $-$ $-$ $+$ \(q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots\)
9408.2.a.de $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(4\) \(0\) $-$ $-$ $-$ \(q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots\)
9408.2.a.df $1$ $75.123$ \(\Q\) None \(0\) \(1\) \(4\) \(0\) $-$ $-$ $-$ \(q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9408.2.a.dg $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(0\) $+$ $+$ $+$ \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.dh $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(0\) $-$ $+$ $+$ \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.di $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(0\) $+$ $+$ $+$ \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots\)
9408.2.a.dj $2$ $75.123$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(-1\) \(0\) $+$ $+$ $-$ \(q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dk $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ \(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots\)
9408.2.a.dl $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ \(q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.dm $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ \(q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots\)
9408.2.a.dn $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ \(q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.do $2$ $75.123$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ \(q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots\)
9408.2.a.dp $2$ $75.123$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(1\) \(0\) $-$ $+$ $+$ \(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.dq $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ \(q-q^{3}+(2+\beta )q^{5}+q^{9}-2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.dr $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $+$ $+$ $+$ \(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.ds $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ \(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dt $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) $-$ $-$ $+$ \(q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots\)
9408.2.a.du $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) $-$ $-$ $+$ \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.dv $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) $+$ $-$ $+$ \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dw $2$ $75.123$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-1\) \(0\) $-$ $-$ $-$ \(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dx $2$ $75.123$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ \(q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9408.2.a.dy $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $+$ \(q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.dz $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ \(q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots\)
9408.2.a.ea $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $+$ \(q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.eb $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ \(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
9408.2.a.ec $2$ $75.123$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(1\) \(0\) $+$ $-$ $+$ \(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.ed $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(0\) $-$ $-$ $+$ \(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.ee $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(0\) $+$ $-$ $+$ \(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.ef $2$ $75.123$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(0\) $+$ $-$ $+$ \(q+q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.eg $3$ $75.123$ 3.3.621.1 None \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ \(q-q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.eh $3$ $75.123$ 3.3.621.1 None \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $+$ \(q-q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ei $3$ $75.123$ 3.3.621.1 None \(0\) \(3\) \(0\) \(0\) $+$ $-$ $-$ \(q+q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ej $3$ $75.123$ 3.3.621.1 None \(0\) \(3\) \(0\) \(0\) $+$ $-$ $+$ \(q+q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.ek $4$ $75.123$ 4.4.2624.1 None \(0\) \(-4\) \(-4\) \(0\) $+$ $+$ $+$ \(q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.el $4$ $75.123$ 4.4.2624.1 None \(0\) \(-4\) \(4\) \(0\) $+$ $+$ $+$ \(q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
9408.2.a.em $4$ $75.123$ 4.4.2624.1 None \(0\) \(4\) \(-4\) \(0\) $+$ $-$ $+$ \(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.en $4$ $75.123$ 4.4.2624.1 None \(0\) \(4\) \(4\) \(0\) $+$ $-$ $+$ \(q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9408))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9408)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4704))\)\(^{\oplus 2}\)