Properties

Label 6336.2.a
Level $6336$
Weight $2$
Character orbit 6336.a
Rep. character $\chi_{6336}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $80$
Sturm bound $2304$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 6336 = 2^{6} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6336.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 80 \)
Sturm bound: \(2304\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(17\), \(19\), \(23\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6336))\).

Total New Old
Modular forms 1200 100 1100
Cusp forms 1105 100 1005
Eisenstein series 95 0 95

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

\(2\)\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(14\)
\(-\)\(-\)\(-\)\(-\)\(17\)
Plus space\(+\)\(47\)
Minus space\(-\)\(53\)

Trace form

\( 100 q + O(q^{10}) \) \( 100 q - 16 q^{13} - 8 q^{17} + 92 q^{25} - 16 q^{37} - 8 q^{41} + 100 q^{49} - 24 q^{53} + 16 q^{61} + 8 q^{73} + 32 q^{85} + 40 q^{89} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6336))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
6336.2.a.a $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) $+$ $-$ $+$ \(q-4q^{5}-2q^{7}-q^{11}-4q^{13}-2q^{17}+\cdots\)
6336.2.a.b $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) $+$ $+$ $+$ \(q-4q^{5}-2q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.c $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) $+$ $-$ $-$ \(q-4q^{5}-2q^{7}+q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.d $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-4\) \(2\) $-$ $-$ $+$ \(q-4q^{5}+2q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.e $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-4\) \(2\) $+$ $-$ $-$ \(q-4q^{5}+2q^{7}+q^{11}-4q^{13}-2q^{17}+\cdots\)
6336.2.a.f $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-4\) \(2\) $-$ $+$ $-$ \(q-4q^{5}+2q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.g $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-3\) \(-4\) $+$ $-$ $-$ \(q-3q^{5}-4q^{7}+q^{11}+2q^{13}+8q^{17}+\cdots\)
6336.2.a.h $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) $+$ $-$ $+$ \(q-3q^{5}-2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
6336.2.a.i $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) $-$ $-$ $-$ \(q-3q^{5}-2q^{7}+q^{11}+4q^{13}-6q^{17}+\cdots\)
6336.2.a.j $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-3\) \(2\) $+$ $-$ $+$ \(q-3q^{5}+2q^{7}-q^{11}+4q^{13}-6q^{17}+\cdots\)
6336.2.a.k $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-3\) \(2\) $-$ $-$ $-$ \(q-3q^{5}+2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
6336.2.a.l $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-3\) \(4\) $+$ $-$ $+$ \(q-3q^{5}+4q^{7}-q^{11}+2q^{13}+8q^{17}+\cdots\)
6336.2.a.m $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $+$ \(q-2q^{5}-4q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
6336.2.a.n $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ \(q-2q^{5}-4q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.o $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $-$ \(q-2q^{5}-4q^{7}+q^{11}-6q^{13}-6q^{17}+\cdots\)
6336.2.a.p $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $-$ \(q-2q^{5}-2q^{7}+q^{11}+2q^{13}+2q^{19}+\cdots\)
6336.2.a.q $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ \(q-2q^{5}-q^{11}-2q^{17}-6q^{19}+6q^{23}+\cdots\)
6336.2.a.r $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ \(q-2q^{5}-q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
6336.2.a.s $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ \(q-2q^{5}+q^{11}-2q^{17}+6q^{19}-6q^{23}+\cdots\)
6336.2.a.t $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ \(q-2q^{5}+q^{11}+6q^{13}-2q^{17}-4q^{19}+\cdots\)
6336.2.a.u $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ \(q-2q^{5}+2q^{7}-q^{11}+2q^{13}-2q^{19}+\cdots\)
6336.2.a.v $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ \(q-2q^{5}+4q^{7}-q^{11}-6q^{13}-6q^{17}+\cdots\)
6336.2.a.w $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $-$ \(q-2q^{5}+4q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots\)
6336.2.a.x $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $-$ \(q-2q^{5}+4q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.y $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ \(q-2q^{7}-q^{11}-4q^{13}+2q^{17}+2q^{23}+\cdots\)
6336.2.a.z $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ \(q-2q^{7}-q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
6336.2.a.ba $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ \(q-2q^{7}-q^{11}+2q^{17}+8q^{19}-2q^{23}+\cdots\)
6336.2.a.bb $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ \(q-2q^{7}-q^{11}+2q^{13}+2q^{17}-6q^{19}+\cdots\)
6336.2.a.bc $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ \(q-2q^{7}-q^{11}+6q^{13}-6q^{17}+2q^{19}+\cdots\)
6336.2.a.bd $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ \(q-2q^{7}+q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
6336.2.a.be $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ \(q-2q^{7}+q^{11}+2q^{13}-2q^{17}-6q^{19}+\cdots\)
6336.2.a.bf $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ \(q-2q^{7}+q^{11}+4q^{13}+6q^{17}-4q^{19}+\cdots\)
6336.2.a.bg $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ \(q-2q^{7}+q^{11}+6q^{13}+6q^{17}+2q^{19}+\cdots\)
6336.2.a.bh $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $+$ \(q+2q^{7}-q^{11}-2q^{13}+6q^{17}-2q^{19}+\cdots\)
6336.2.a.bi $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $+$ \(q+2q^{7}-q^{11}+2q^{13}-2q^{17}+6q^{19}+\cdots\)
6336.2.a.bj $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ \(q+2q^{7}-q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots\)
6336.2.a.bk $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ \(q+2q^{7}-q^{11}+6q^{13}+6q^{17}-2q^{19}+\cdots\)
6336.2.a.bl $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ \(q+2q^{7}+q^{11}-4q^{13}+2q^{17}-2q^{23}+\cdots\)
6336.2.a.bm $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ \(q+2q^{7}+q^{11}-2q^{13}-6q^{17}-2q^{19}+\cdots\)
6336.2.a.bn $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ \(q+2q^{7}+q^{11}+2q^{17}-8q^{19}+2q^{23}+\cdots\)
6336.2.a.bo $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ \(q+2q^{7}+q^{11}+2q^{13}+2q^{17}+6q^{19}+\cdots\)
6336.2.a.bp $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ \(q+2q^{7}+q^{11}+6q^{13}-6q^{17}-2q^{19}+\cdots\)
6336.2.a.bq $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $+$ \(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{19}+\cdots\)
6336.2.a.br $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ \(q+q^{5}-2q^{7}+q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.bs $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $+$ \(q+q^{5}-q^{11}+6q^{13}+4q^{17}-6q^{19}+\cdots\)
6336.2.a.bt $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ \(q+q^{5}+q^{11}+6q^{13}+4q^{17}+6q^{19}+\cdots\)
6336.2.a.bu $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $+$ \(q+q^{5}+2q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
6336.2.a.bv $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ \(q+q^{5}+4q^{7}+q^{11}+2q^{13}+2q^{19}+\cdots\)
6336.2.a.bw $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $+$ \(q+2q^{5}-4q^{7}-q^{11}+6q^{13}-2q^{17}+\cdots\)
6336.2.a.bx $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $-$ $+$ $-$ \(q+2q^{5}-4q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots\)
6336.2.a.by $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ \(q+2q^{5}-4q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.bz $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ \(q+2q^{5}-2q^{7}+q^{11}-6q^{13}+4q^{17}+\cdots\)
6336.2.a.ca $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ \(q+2q^{5}-2q^{7}+q^{11}+2q^{13}-4q^{17}+\cdots\)
6336.2.a.cb $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ \(q+2q^{5}-q^{11}-2q^{13}-6q^{17}+4q^{23}+\cdots\)
6336.2.a.cc $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $+$ \(q+2q^{5}-q^{11}+2q^{17}+6q^{19}+6q^{23}+\cdots\)
6336.2.a.cd $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ \(q+2q^{5}+q^{11}-2q^{13}-6q^{17}-4q^{23}+\cdots\)
6336.2.a.ce $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ \(q+2q^{5}+q^{11}+2q^{17}-6q^{19}-6q^{23}+\cdots\)
6336.2.a.cf $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $+$ \(q+2q^{5}+2q^{7}-q^{11}-6q^{13}+4q^{17}+\cdots\)
6336.2.a.cg $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $+$ \(q+2q^{5}+2q^{7}-q^{11}+2q^{13}-4q^{17}+\cdots\)
6336.2.a.ch $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $-$ $+$ $+$ \(q+2q^{5}+4q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
6336.2.a.ci $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $+$ $-$ $+$ \(q+2q^{5}+4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
6336.2.a.cj $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ \(q+2q^{5}+4q^{7}+q^{11}+6q^{13}-2q^{17}+\cdots\)
6336.2.a.ck $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(4\) \(-2\) $+$ $-$ $+$ \(q+4q^{5}-2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
6336.2.a.cl $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(4\) \(-2\) $+$ $+$ $-$ \(q+4q^{5}-2q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.cm $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(4\) \(2\) $-$ $+$ $+$ \(q+4q^{5}+2q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
6336.2.a.cn $1$ $50.593$ \(\Q\) None \(0\) \(0\) \(4\) \(2\) $-$ $-$ $-$ \(q+4q^{5}+2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
6336.2.a.co $2$ $50.593$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ \(q+\beta q^{5}+(-2-\beta )q^{7}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
6336.2.a.cp $2$ $50.593$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ \(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
6336.2.a.cq $2$ $50.593$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $+$ \(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
6336.2.a.cr $2$ $50.593$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ \(q+\beta q^{5}+(2+\beta )q^{7}+q^{11}+(-2+\beta )q^{13}+\cdots\)
6336.2.a.cs $2$ $50.593$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{11}+(-3+\cdots)q^{13}+\cdots\)
6336.2.a.ct $2$ $50.593$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $+$ \(q+(1+\beta )q^{5}+(1-\beta )q^{7}-q^{11}+(-3+\cdots)q^{13}+\cdots\)
6336.2.a.cu $2$ $50.593$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $+$ $-$ $+$ \(q+(1+\beta )q^{5}+(-2+2\beta )q^{7}-q^{11}+\cdots\)
6336.2.a.cv $2$ $50.593$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(0\) $+$ $-$ $+$ \(q+(1+\beta )q^{5}-q^{11}-2q^{13}+(-4+2\beta )q^{17}+\cdots\)
6336.2.a.cw $2$ $50.593$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(0\) $+$ $-$ $-$ \(q+(1+\beta )q^{5}+q^{11}-2q^{13}+(-4+2\beta )q^{17}+\cdots\)
6336.2.a.cx $2$ $50.593$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(2\) $-$ $-$ $-$ \(q+(1+\beta )q^{5}+(2-2\beta )q^{7}+q^{11}+2\beta q^{13}+\cdots\)
6336.2.a.cy $3$ $50.593$ 3.3.229.1 None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ \(q-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}-q^{11}+\beta _{1}q^{13}+\cdots\)
6336.2.a.cz $3$ $50.593$ 3.3.229.1 None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $-$ \(q-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{11}+\beta _{1}q^{13}+\cdots\)
6336.2.a.da $4$ $50.593$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ \(q+\beta _{1}q^{5}+\beta _{3}q^{7}-q^{11}+(-2-\beta _{2}+\cdots)q^{13}+\cdots\)
6336.2.a.db $4$ $50.593$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{11}+(-2+\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6336))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6336)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1056))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3168))\)\(^{\oplus 2}\)