Properties

Label 9295.2.a
Level $9295$
Weight $2$
Character orbit 9295.a
Rep. character $\chi_{9295}(1,\cdot)$
Character field $\Q$
Dimension $518$
Newform subspaces $41$
Sturm bound $2184$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9295.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 41 \)
Sturm bound: \(2184\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9295))\).

Total New Old
Modular forms 1120 518 602
Cusp forms 1065 518 547
Eisenstein series 55 0 55

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

\(5\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(63\)
\(+\)\(+\)\(-\)\(-\)\(68\)
\(+\)\(-\)\(+\)\(-\)\(73\)
\(+\)\(-\)\(-\)\(+\)\(56\)
\(-\)\(+\)\(+\)\(-\)\(66\)
\(-\)\(+\)\(-\)\(+\)\(62\)
\(-\)\(-\)\(+\)\(+\)\(56\)
\(-\)\(-\)\(-\)\(-\)\(74\)
Plus space\(+\)\(237\)
Minus space\(-\)\(281\)

Trace form

\( 518 q + 4 q^{3} + 518 q^{4} - 2 q^{5} + 4 q^{6} + 12 q^{7} + 12 q^{8} + 518 q^{9} + O(q^{10}) \) \( 518 q + 4 q^{3} + 518 q^{4} - 2 q^{5} + 4 q^{6} + 12 q^{7} + 12 q^{8} + 518 q^{9} - 4 q^{10} + 4 q^{12} - 20 q^{14} - 4 q^{15} + 522 q^{16} - 4 q^{17} - 8 q^{18} - 2 q^{20} + 2 q^{22} + 12 q^{23} - 20 q^{24} + 518 q^{25} + 40 q^{27} + 60 q^{28} - 20 q^{29} - 4 q^{30} + 16 q^{31} + 24 q^{32} - 4 q^{33} - 24 q^{34} - 4 q^{35} + 542 q^{36} + 12 q^{37} + 48 q^{38} - 24 q^{40} - 12 q^{41} + 24 q^{42} + 44 q^{43} + 4 q^{44} - 10 q^{45} - 4 q^{46} - 4 q^{47} + 44 q^{48} + 534 q^{49} - 40 q^{51} - 20 q^{53} + 32 q^{54} + 4 q^{55} - 28 q^{56} + 48 q^{57} + 16 q^{58} + 24 q^{59} - 12 q^{60} + 4 q^{61} + 16 q^{62} + 12 q^{63} + 574 q^{64} + 20 q^{66} + 20 q^{67} - 20 q^{68} - 16 q^{69} - 12 q^{70} - 32 q^{71} + 76 q^{72} + 28 q^{73} + 104 q^{74} + 4 q^{75} - 24 q^{76} + 4 q^{77} + 16 q^{79} + 10 q^{80} + 486 q^{81} + 96 q^{82} - 68 q^{83} + 72 q^{84} - 20 q^{85} + 44 q^{86} + 40 q^{87} + 6 q^{88} + 12 q^{89} + 20 q^{90} + 156 q^{92} + 48 q^{93} + 60 q^{94} + 8 q^{95} - 68 q^{96} + 4 q^{97} - 40 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9295))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11 13
9295.2.a.a $1$ $74.221$ \(\Q\) None \(-2\) \(-2\) \(1\) \(-4\) $-$ $-$ $-$ \(q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots\)
9295.2.a.b $1$ $74.221$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}-3q^{9}+q^{10}+\cdots\)
9295.2.a.c $1$ $74.221$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-2\) $+$ $-$ $+$ \(q-2q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
9295.2.a.d $1$ $74.221$ \(\Q\) None \(2\) \(-2\) \(-1\) \(4\) $+$ $+$ $-$ \(q+2q^{2}-2q^{3}+2q^{4}-q^{5}-4q^{6}+\cdots\)
9295.2.a.e $1$ $74.221$ \(\Q\) None \(2\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ \(q+2q^{2}+2q^{4}-q^{5}-3q^{9}-2q^{10}+\cdots\)
9295.2.a.f $2$ $74.221$ \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-2\) \(4\) $+$ $+$ $+$ \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
9295.2.a.g $2$ $74.221$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) $-$ $+$ $+$ \(q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
9295.2.a.h $2$ $74.221$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ \(q+\beta q^{2}+\beta q^{3}-q^{5}+2q^{6}+(2+\beta )q^{7}+\cdots\)
9295.2.a.i $2$ $74.221$ \(\Q(\sqrt{5}) \) None \(3\) \(-3\) \(2\) \(-4\) $-$ $-$ $+$ \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
9295.2.a.j $3$ $74.221$ 3.3.148.1 None \(-2\) \(0\) \(3\) \(4\) $-$ $-$ $+$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9295.2.a.k $3$ $74.221$ 3.3.148.1 None \(0\) \(2\) \(3\) \(-6\) $-$ $+$ $+$ \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
9295.2.a.l $4$ $74.221$ 4.4.4752.1 None \(-2\) \(-2\) \(4\) \(2\) $-$ $+$ $-$ \(q-\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
9295.2.a.m $4$ $74.221$ 4.4.4752.1 None \(2\) \(-2\) \(-4\) \(-2\) $+$ $-$ $-$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.n $6$ $74.221$ 6.6.37261816.1 None \(1\) \(-4\) \(6\) \(-2\) $-$ $-$ $+$ \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9295.2.a.o $6$ $74.221$ 6.6.3486377.1 None \(5\) \(-2\) \(6\) \(8\) $-$ $+$ $+$ \(q+(1-\beta _{4})q^{2}-\beta _{5}q^{3}+(1+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
9295.2.a.p $8$ $74.221$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(8\) \(-1\) $-$ $-$ $+$ \(q+(-1-\beta _{2})q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
9295.2.a.q $8$ $74.221$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(0\) \(-8\) \(-2\) $+$ $+$ $+$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.r $8$ $74.221$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(-8\) \(1\) $+$ $+$ $+$ \(q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
9295.2.a.s $9$ $74.221$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-1\) \(0\) \(9\) \(-4\) $-$ $+$ $-$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
9295.2.a.t $9$ $74.221$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-1\) \(2\) \(-9\) \(4\) $+$ $-$ $+$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.u $9$ $74.221$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(1\) \(0\) \(-9\) \(4\) $+$ $-$ $-$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.v $10$ $74.221$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(-3\) \(10\) \(-3\) $-$ $-$ $+$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
9295.2.a.w $10$ $74.221$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-3\) \(-10\) \(3\) $+$ $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.x $12$ $74.221$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(6\) \(-12\) \(-8\) $+$ $+$ $-$ \(q-\beta _{1}q^{2}+(1+\beta _{7})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9295.2.a.y $12$ $74.221$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(6\) \(12\) \(8\) $-$ $-$ $-$ \(q+\beta _{1}q^{2}+(1+\beta _{7})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9295.2.a.z $14$ $74.221$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-1\) \(1\) \(-14\) \(-3\) $+$ $-$ $+$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.ba $14$ $74.221$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-1\) \(1\) \(-14\) \(-5\) $+$ $-$ $+$ \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.bb $14$ $74.221$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(1\) \(14\) \(5\) $-$ $+$ $+$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
9295.2.a.bc $14$ $74.221$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(1\) \(14\) \(3\) $-$ $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
9295.2.a.bd $16$ $74.221$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-16\) \(10\) $+$ $-$ $-$ \(q-\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
9295.2.a.be $16$ $74.221$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(16\) \(-10\) $-$ $+$ $-$ \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
9295.2.a.bf $27$ $74.221$ None \(-10\) \(-12\) \(27\) \(-8\) $-$ $-$ $+$
9295.2.a.bg $27$ $74.221$ None \(-8\) \(0\) \(-27\) \(-6\) $+$ $-$ $-$
9295.2.a.bh $27$ $74.221$ None \(8\) \(0\) \(27\) \(6\) $-$ $+$ $+$
9295.2.a.bi $27$ $74.221$ None \(10\) \(-12\) \(-27\) \(8\) $+$ $+$ $-$
9295.2.a.bj $28$ $74.221$ None \(-2\) \(6\) \(-28\) \(-8\) $+$ $+$ $-$
9295.2.a.bk $28$ $74.221$ None \(2\) \(6\) \(28\) \(8\) $-$ $-$ $-$
9295.2.a.bl $33$ $74.221$ None \(-10\) \(0\) \(33\) \(-6\) $-$ $+$ $-$
9295.2.a.bm $33$ $74.221$ None \(-8\) \(12\) \(-33\) \(-4\) $+$ $+$ $+$
9295.2.a.bn $33$ $74.221$ None \(8\) \(12\) \(33\) \(4\) $-$ $-$ $-$
9295.2.a.bo $33$ $74.221$ None \(10\) \(0\) \(-33\) \(6\) $+$ $-$ $+$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9295))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9295)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(715))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1859))\)\(^{\oplus 2}\)