Properties

Label 2695.2.a
Level $2695$
Weight $2$
Character orbit 2695.a
Rep. character $\chi_{2695}(1,\cdot)$
Character field $\Q$
Dimension $138$
Newform subspaces $26$
Sturm bound $672$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(672\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2695))\).

Total New Old
Modular forms 352 138 214
Cusp forms 321 138 183
Eisenstein series 31 0 31

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

\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(16\)
\(+\)\(+\)\(-\)\(-\)\(20\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(59\)
Minus space\(-\)\(79\)

Trace form

\( 138 q + 4 q^{3} + 138 q^{4} + 2 q^{5} - 12 q^{6} - 12 q^{8} + 146 q^{9} + O(q^{10}) \) \( 138 q + 4 q^{3} + 138 q^{4} + 2 q^{5} - 12 q^{6} - 12 q^{8} + 146 q^{9} - 4 q^{10} + 20 q^{12} + 20 q^{13} - 4 q^{15} + 142 q^{16} - 4 q^{17} + 8 q^{18} + 10 q^{20} - 2 q^{22} - 20 q^{23} - 4 q^{24} + 138 q^{25} + 8 q^{26} - 8 q^{27} + 12 q^{29} + 4 q^{30} + 16 q^{31} + 16 q^{32} + 4 q^{33} - 8 q^{34} + 162 q^{36} - 28 q^{37} + 40 q^{38} - 48 q^{39} - 24 q^{40} - 12 q^{41} - 12 q^{43} + 4 q^{44} + 10 q^{45} + 20 q^{46} + 36 q^{47} + 52 q^{48} + 56 q^{51} + 20 q^{52} - 4 q^{53} - 16 q^{54} + 4 q^{55} - 24 q^{57} + 8 q^{58} - 32 q^{59} - 12 q^{60} + 20 q^{61} - 48 q^{62} + 74 q^{64} - 4 q^{65} + 20 q^{66} - 28 q^{67} + 28 q^{68} - 32 q^{69} + 8 q^{71} + 36 q^{72} + 28 q^{73} + 40 q^{74} + 4 q^{75} + 64 q^{78} - 64 q^{79} + 6 q^{80} + 202 q^{81} - 40 q^{82} + 12 q^{83} - 12 q^{85} + 84 q^{86} - 40 q^{87} - 6 q^{88} - 4 q^{89} + 20 q^{90} + 36 q^{92} - 72 q^{93} - 52 q^{94} + 8 q^{95} + 84 q^{96} + 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2695))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 11
2695.2.a.a $1$ $21.520$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $-$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}-3q^{9}+q^{10}+\cdots\)
2695.2.a.b $1$ $21.520$ \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) $+$ $-$ $+$ \(q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+3q^{8}+\cdots\)
2695.2.a.c $1$ $21.520$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-3q^{9}-q^{10}+\cdots\)
2695.2.a.d $2$ $21.520$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $+$ \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}+q^{5}+(-3+\cdots)q^{6}+\cdots\)
2695.2.a.e $2$ $21.520$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
2695.2.a.f $2$ $21.520$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ \(q+(1+\beta )q^{2}+2\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
2695.2.a.g $3$ $21.520$ 3.3.148.1 None \(-3\) \(2\) \(3\) \(0\) $-$ $-$ $+$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
2695.2.a.h $3$ $21.520$ 3.3.148.1 None \(-3\) \(4\) \(3\) \(0\) $-$ $-$ $-$ \(q+(-1-\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
2695.2.a.i $3$ $21.520$ 3.3.148.1 None \(1\) \(0\) \(-3\) \(0\) $+$ $-$ $-$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
2695.2.a.j $4$ $21.520$ 4.4.1957.1 None \(-3\) \(-3\) \(4\) \(0\) $-$ $+$ $-$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\cdots\)
2695.2.a.k $4$ $21.520$ 4.4.1957.1 None \(-3\) \(3\) \(-4\) \(0\) $+$ $-$ $-$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\cdots\)
2695.2.a.l $4$ $21.520$ 4.4.11348.1 None \(2\) \(-2\) \(-4\) \(0\) $+$ $-$ $+$ \(q+(1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots\)
2695.2.a.m $5$ $21.520$ 5.5.303952.1 None \(-1\) \(0\) \(-5\) \(0\) $+$ $-$ $+$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots\)
2695.2.a.n $5$ $21.520$ 5.5.303952.1 None \(-1\) \(0\) \(5\) \(0\) $-$ $-$ $+$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots\)
2695.2.a.o $5$ $21.520$ 5.5.394064.1 None \(1\) \(-4\) \(-5\) \(0\) $+$ $-$ $-$ \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2695.2.a.p $5$ $21.520$ 5.5.394064.1 None \(1\) \(4\) \(5\) \(0\) $-$ $-$ $-$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2695.2.a.q $6$ $21.520$ 6.6.15751800.1 None \(-3\) \(-1\) \(6\) \(0\) $-$ $-$ $+$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\cdots\)
2695.2.a.r $6$ $21.520$ 6.6.15751800.1 None \(-3\) \(1\) \(-6\) \(0\) $+$ $+$ $+$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\cdots\)
2695.2.a.s $8$ $21.520$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(-1\) \(-8\) \(0\) $+$ $-$ $+$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2695.2.a.t $8$ $21.520$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(1\) \(8\) \(0\) $-$ $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2695.2.a.u $10$ $21.520$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-8\) \(10\) \(0\) $-$ $+$ $-$ \(q-\beta _{1}q^{2}+(-1-\beta _{9})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2695.2.a.v $10$ $21.520$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(8\) \(-10\) \(0\) $+$ $+$ $-$ \(q-\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2695.2.a.w $10$ $21.520$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(-10\) \(0\) $+$ $+$ $+$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2695.2.a.x $10$ $21.520$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(10\) \(0\) $-$ $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2695.2.a.y $10$ $21.520$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-3\) \(-10\) \(0\) $+$ $+$ $-$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
2695.2.a.z $10$ $21.520$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(3\) \(10\) \(0\) $-$ $-$ $-$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2695))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2695)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 2}\)