Properties

Label 9680.2.a
Level $9680$
Weight $2$
Character orbit 9680.a
Rep. character $\chi_{9680}(1,\cdot)$
Character field $\Q$
Dimension $218$
Newform subspaces $84$
Sturm bound $3168$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9680.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 84 \)
Sturm bound: \(3168\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9680))\).

Total New Old
Modular forms 1656 218 1438
Cusp forms 1513 218 1295
Eisenstein series 143 0 143

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

\(2\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(24\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(30\)
\(+\)\(-\)\(-\)\(+\)\(25\)
\(-\)\(+\)\(+\)\(-\)\(30\)
\(-\)\(+\)\(-\)\(+\)\(25\)
\(-\)\(-\)\(+\)\(+\)\(24\)
\(-\)\(-\)\(-\)\(-\)\(30\)
Plus space\(+\)\(98\)
Minus space\(-\)\(120\)

Trace form

\( 218 q + 2 q^{3} + 6 q^{7} + 222 q^{9} + O(q^{10}) \) \( 218 q + 2 q^{3} + 6 q^{7} + 222 q^{9} - 2 q^{15} + 4 q^{17} - 4 q^{21} - 2 q^{23} + 218 q^{25} - 4 q^{27} - 12 q^{29} + 12 q^{31} - 6 q^{35} - 8 q^{37} - 20 q^{39} + 14 q^{43} - 4 q^{45} - 22 q^{47} + 230 q^{49} - 36 q^{51} + 8 q^{57} - 16 q^{59} + 16 q^{61} + 6 q^{63} + 4 q^{65} + 30 q^{67} + 20 q^{69} + 12 q^{71} + 20 q^{73} + 2 q^{75} + 8 q^{79} + 230 q^{81} - 26 q^{83} + 8 q^{85} - 36 q^{87} + 20 q^{89} + 52 q^{91} + 40 q^{93} + 8 q^{95} + 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9680))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11
9680.2.a.a $1$ $77.295$ \(\Q\) None \(0\) \(-3\) \(1\) \(1\) $+$ $-$ $-$ \(q-3q^{3}+q^{5}+q^{7}+6q^{9}+6q^{13}+\cdots\)
9680.2.a.b $1$ $77.295$ \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) $-$ $+$ $+$ \(q-2q^{3}-q^{5}+q^{9}-6q^{13}+2q^{15}+\cdots\)
9680.2.a.c $1$ $77.295$ \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) $-$ $+$ $+$ \(q-2q^{3}-q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
9680.2.a.d $1$ $77.295$ \(\Q\) None \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $-$ \(q-2q^{3}+q^{5}+q^{9}-2q^{15}+4q^{17}+\cdots\)
9680.2.a.e $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ \(q-q^{3}-q^{5}-3q^{7}-2q^{9}-4q^{13}+\cdots\)
9680.2.a.f $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $-$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{13}+q^{15}+\cdots\)
9680.2.a.g $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $-$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{13}+q^{15}+\cdots\)
9680.2.a.h $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $-$ \(q-q^{3}-q^{5}+q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
9680.2.a.i $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) $+$ $+$ $+$ \(q-q^{3}-q^{5}+3q^{7}-2q^{9}+4q^{13}+\cdots\)
9680.2.a.j $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(-1\) \(5\) $-$ $+$ $-$ \(q-q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{13}+\cdots\)
9680.2.a.k $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $-$ $-$ \(q-q^{3}+q^{5}-q^{7}-2q^{9}+4q^{13}-q^{15}+\cdots\)
9680.2.a.l $1$ $77.295$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $-$ $-$ \(q-q^{3}+q^{5}+q^{7}-2q^{9}-4q^{13}-q^{15}+\cdots\)
9680.2.a.m $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $+$ $+$ \(q-q^{5}-4q^{7}-3q^{9}+4q^{13}-4q^{17}+\cdots\)
9680.2.a.n $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $-$ \(q-q^{5}-2q^{7}-3q^{9}-8q^{19}+8q^{23}+\cdots\)
9680.2.a.o $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $-$ \(q-q^{5}-2q^{7}-3q^{9}+4q^{13}+4q^{17}+\cdots\)
9680.2.a.p $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ \(q-q^{5}+4q^{7}-3q^{9}-4q^{13}+4q^{17}+\cdots\)
9680.2.a.q $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ \(q+q^{5}-4q^{7}-3q^{9}+2q^{13}-2q^{17}+\cdots\)
9680.2.a.r $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ \(q+q^{5}-3q^{9}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
9680.2.a.s $1$ $77.295$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $+$ $-$ $-$ \(q+q^{5}+4q^{7}-3q^{9}-6q^{13}+6q^{17}+\cdots\)
9680.2.a.t $1$ $77.295$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ \(q+q^{3}+q^{5}-3q^{7}-2q^{9}+q^{15}-8q^{17}+\cdots\)
9680.2.a.u $1$ $77.295$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $+$ \(q+q^{3}+q^{5}-3q^{7}-2q^{9}+q^{15}+3q^{17}+\cdots\)
9680.2.a.v $1$ $77.295$ \(\Q\) None \(0\) \(1\) \(1\) \(3\) $-$ $-$ $+$ \(q+q^{3}+q^{5}+3q^{7}-2q^{9}+q^{15}-3q^{17}+\cdots\)
9680.2.a.w $1$ $77.295$ \(\Q\) None \(0\) \(1\) \(1\) \(3\) $-$ $-$ $-$ \(q+q^{3}+q^{5}+3q^{7}-2q^{9}+q^{15}+8q^{17}+\cdots\)
9680.2.a.x $1$ $77.295$ \(\Q\) None \(0\) \(1\) \(1\) \(3\) $-$ $-$ $-$ \(q+q^{3}+q^{5}+3q^{7}-2q^{9}+6q^{13}+\cdots\)
9680.2.a.y $1$ $77.295$ \(\Q\) None \(0\) \(2\) \(-1\) \(0\) $+$ $+$ $+$ \(q+2q^{3}-q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9680.2.a.z $1$ $77.295$ \(\Q\) None \(0\) \(2\) \(-1\) \(0\) $+$ $+$ $+$ \(q+2q^{3}-q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
9680.2.a.ba $1$ $77.295$ \(\Q\) None \(0\) \(2\) \(-1\) \(2\) $-$ $+$ $-$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
9680.2.a.bb $1$ $77.295$ \(\Q\) None \(0\) \(2\) \(1\) \(-4\) $-$ $-$ $-$ \(q+2q^{3}+q^{5}-4q^{7}+q^{9}+4q^{13}+\cdots\)
9680.2.a.bc $1$ $77.295$ \(\Q\) None \(0\) \(3\) \(-1\) \(-5\) $-$ $+$ $+$ \(q+3q^{3}-q^{5}-5q^{7}+6q^{9}-4q^{13}+\cdots\)
9680.2.a.bd $1$ $77.295$ \(\Q\) None \(0\) \(3\) \(-1\) \(5\) $-$ $+$ $+$ \(q+3q^{3}-q^{5}+5q^{7}+6q^{9}+4q^{13}+\cdots\)
9680.2.a.be $1$ $77.295$ \(\Q\) None \(0\) \(3\) \(1\) \(-3\) $-$ $-$ $-$ \(q+3q^{3}+q^{5}-3q^{7}+6q^{9}-4q^{13}+\cdots\)
9680.2.a.bf $1$ $77.295$ \(\Q\) None \(0\) \(3\) \(1\) \(3\) $-$ $-$ $-$ \(q+3q^{3}+q^{5}+3q^{7}+6q^{9}+4q^{13}+\cdots\)
9680.2.a.bg $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(2\) \(0\) $-$ $-$ $+$ \(q-2q^{3}+q^{5}+\beta q^{7}+q^{9}-2q^{15}+\cdots\)
9680.2.a.bh $2$ $77.295$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-3\) $-$ $+$ $+$ \(q-2\beta q^{3}-q^{5}+(-1-\beta )q^{7}+(1+4\beta )q^{9}+\cdots\)
9680.2.a.bi $2$ $77.295$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(3\) $-$ $+$ $-$ \(q-2\beta q^{3}-q^{5}+(1+\beta )q^{7}+(1+4\beta )q^{9}+\cdots\)
9680.2.a.bj $2$ $77.295$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(-2\) $+$ $-$ $-$ \(q+(-1+\beta )q^{3}+q^{5}+(-1+\beta )q^{7}+\cdots\)
9680.2.a.bk $2$ $77.295$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $-$ $-$ \(q+(-1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}-2\beta q^{9}+\cdots\)
9680.2.a.bl $2$ $77.295$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(3\) $+$ $+$ $-$ \(q-\beta q^{3}-q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
9680.2.a.bm $2$ $77.295$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(5\) $+$ $+$ $-$ \(q-\beta q^{3}-q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
9680.2.a.bn $2$ $77.295$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $-$ \(q+\beta q^{3}-q^{5}-2q^{7}+5q^{9}+(4-\beta )q^{13}+\cdots\)
9680.2.a.bo $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ \(q+\beta q^{3}-q^{5}+(-1-2\beta )q^{7}+(-2+\cdots)q^{13}+\cdots\)
9680.2.a.bp $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ \(q+\beta q^{3}-q^{5}+(1+2\beta )q^{7}+(2+2\beta )q^{13}+\cdots\)
9680.2.a.bq $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ \(q+\beta q^{3}+q^{5}+(-2+\beta )q^{7}+2\beta q^{13}+\cdots\)
9680.2.a.br $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(4\) $+$ $-$ $-$ \(q+\beta q^{3}+q^{5}+(2-\beta )q^{7}-2\beta q^{13}+\cdots\)
9680.2.a.bs $2$ $77.295$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(-1\) $+$ $-$ $-$ \(q+\beta q^{3}+q^{5}-\beta q^{7}+(1+\beta )q^{9}-2q^{13}+\cdots\)
9680.2.a.bt $2$ $77.295$ \(\Q(\sqrt{33}) \) None \(0\) \(1\) \(2\) \(1\) $-$ $-$ $-$ \(q+\beta q^{3}+q^{5}+\beta q^{7}+(5+\beta )q^{9}-2q^{13}+\cdots\)
9680.2.a.bu $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ \(q+q^{3}-q^{5}-\beta q^{7}-2q^{9}-2\beta q^{13}+\cdots\)
9680.2.a.bv $2$ $77.295$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $+$ \(q+q^{3}+q^{5}-\beta q^{7}-2q^{9}+q^{15}+4\beta q^{19}+\cdots\)
9680.2.a.bw $2$ $77.295$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(0\) $-$ $+$ $-$ \(q+(1+\beta )q^{3}-q^{5}+(-1+3\beta )q^{9}+(-4+\cdots)q^{13}+\cdots\)
9680.2.a.bx $2$ $77.295$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(0\) $-$ $+$ $+$ \(q+(1+\beta )q^{3}-q^{5}+(-1+3\beta )q^{9}+(4+\cdots)q^{13}+\cdots\)
9680.2.a.by $3$ $77.295$ 3.3.788.1 None \(0\) \(-1\) \(-3\) \(-3\) $+$ $+$ $-$ \(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9680.2.a.bz $3$ $77.295$ 3.3.404.1 None \(0\) \(-1\) \(-3\) \(-1\) $-$ $+$ $-$ \(q-\beta _{1}q^{3}-q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.ca $3$ $77.295$ 3.3.404.1 None \(0\) \(-1\) \(-3\) \(-1\) $+$ $+$ $-$ \(q-\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
9680.2.a.cb $3$ $77.295$ 3.3.404.1 None \(0\) \(-1\) \(-3\) \(1\) $-$ $+$ $-$ \(q-\beta _{1}q^{3}-q^{5}+(2\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.cc $3$ $77.295$ 3.3.404.1 None \(0\) \(-1\) \(-3\) \(1\) $+$ $+$ $-$ \(q-\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
9680.2.a.cd $3$ $77.295$ 3.3.788.1 None \(0\) \(-1\) \(-3\) \(3\) $+$ $+$ $-$ \(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9680.2.a.ce $3$ $77.295$ 3.3.1524.1 None \(0\) \(-1\) \(3\) \(-1\) $-$ $-$ $-$ \(q-\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9680.2.a.cf $3$ $77.295$ 3.3.1524.1 None \(0\) \(-1\) \(3\) \(1\) $-$ $-$ $-$ \(q-\beta _{1}q^{3}+q^{5}-\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9680.2.a.cg $3$ $77.295$ 3.3.568.1 None \(0\) \(1\) \(3\) \(-1\) $+$ $-$ $+$ \(q-\beta _{2}q^{3}+q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
9680.2.a.ch $3$ $77.295$ 3.3.568.1 None \(0\) \(1\) \(3\) \(1\) $+$ $-$ $+$ \(q-\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
9680.2.a.ci $4$ $77.295$ 4.4.5225.1 None \(0\) \(-3\) \(4\) \(-3\) $-$ $-$ $-$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cj $4$ $77.295$ 4.4.5225.1 None \(0\) \(-3\) \(4\) \(3\) $-$ $-$ $+$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots\)
9680.2.a.ck $4$ $77.295$ 4.4.5125.1 None \(0\) \(-2\) \(-4\) \(-3\) $-$ $+$ $+$ \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
9680.2.a.cl $4$ $77.295$ 4.4.5125.1 None \(0\) \(-2\) \(-4\) \(3\) $-$ $+$ $-$ \(q-\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cm $4$ $77.295$ 4.4.725.1 None \(0\) \(0\) \(-4\) \(-3\) $-$ $+$ $-$ \(q+(\beta _{2}-\beta _{3})q^{3}-q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.cn $4$ $77.295$ 4.4.725.1 None \(0\) \(0\) \(-4\) \(3\) $-$ $+$ $+$ \(q+(\beta _{2}-\beta _{3})q^{3}-q^{5}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.co $4$ $77.295$ 4.4.2525.1 None \(0\) \(0\) \(4\) \(-3\) $-$ $-$ $-$ \(q+(\beta _{1}+\beta _{2})q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.cp $4$ $77.295$ 4.4.2525.1 None \(0\) \(0\) \(4\) \(3\) $-$ $-$ $+$ \(q+(\beta _{1}+\beta _{2})q^{3}+q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.cq $4$ $77.295$ 4.4.4752.1 None \(0\) \(2\) \(-4\) \(-6\) $+$ $+$ $+$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-2-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cr $4$ $77.295$ 4.4.4752.1 None \(0\) \(2\) \(-4\) \(6\) $+$ $+$ $+$ \(q+(1+\beta _{2})q^{3}-q^{5}+(2+\beta _{2}-\beta _{3})q^{7}+\cdots\)
9680.2.a.cs $4$ $77.295$ 4.4.2525.1 None \(0\) \(2\) \(4\) \(-11\) $-$ $-$ $+$ \(q+\beta _{1}q^{3}+q^{5}+(-3-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.ct $4$ $77.295$ 4.4.725.1 None \(0\) \(2\) \(4\) \(-7\) $+$ $-$ $-$ \(q+\beta _{2}q^{3}+q^{5}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
9680.2.a.cu $4$ $77.295$ 4.4.725.1 None \(0\) \(2\) \(4\) \(7\) $+$ $-$ $+$ \(q+\beta _{2}q^{3}+q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cv $4$ $77.295$ 4.4.2525.1 None \(0\) \(2\) \(4\) \(11\) $-$ $-$ $-$ \(q+\beta _{1}q^{3}+q^{5}+(3+\beta _{2}-\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.cw $6$ $77.295$ 6.6.27433728.1 None \(0\) \(-6\) \(6\) \(0\) $-$ $-$ $+$ \(q+(-1+\beta _{3})q^{3}+q^{5}-\beta _{1}q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
9680.2.a.cx $6$ $77.295$ 6.6.45753625.1 None \(0\) \(-2\) \(-6\) \(-6\) $+$ $+$ $+$ \(q+\beta _{3}q^{3}-q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+\cdots\)
9680.2.a.cy $6$ $77.295$ 6.6.45753625.1 None \(0\) \(-2\) \(-6\) \(6\) $+$ $+$ $-$ \(q+\beta _{3}q^{3}-q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{9}+\cdots\)
9680.2.a.cz $6$ $77.295$ 6.6.507624192.1 None \(0\) \(2\) \(-6\) \(0\) $-$ $+$ $+$ \(q+\beta _{4}q^{3}-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
9680.2.a.da $6$ $77.295$ 6.6.22733568.1 None \(0\) \(2\) \(6\) \(-4\) $+$ $-$ $+$ \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.db $6$ $77.295$ 6.6.22733568.1 None \(0\) \(2\) \(6\) \(4\) $+$ $-$ $+$ \(q-\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.dc $6$ $77.295$ 6.6.25903625.1 None \(0\) \(3\) \(-6\) \(-7\) $+$ $+$ $+$ \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
9680.2.a.dd $6$ $77.295$ 6.6.25903625.1 None \(0\) \(3\) \(-6\) \(7\) $+$ $+$ $-$ \(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots\)
9680.2.a.de $8$ $77.295$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(8\) \(-6\) $+$ $-$ $-$ \(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)
9680.2.a.df $8$ $77.295$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(8\) \(6\) $+$ $-$ $+$ \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9680))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9680)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4840))\)\(^{\oplus 2}\)