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Properties

Label 2695.1
Level 2695
Weight 1
Dimension 199
Nonzero newspaces 9
Newform subspaces 30
Sturm bound 564480
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 30 \)
Sturm bound: \(564480\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2695))\).

Total New Old
Modular forms 5108 2817 2291
Cusp forms 308 199 109
Eisenstein series 4800 2618 2182

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 199 0 0 0

Trace form

\( 199 q + 7 q^{4} + q^{5} - q^{9} + O(q^{10}) \) \( 199 q + 7 q^{4} + q^{5} - q^{9} + 3 q^{11} - 12 q^{14} - 6 q^{15} - 11 q^{16} + 7 q^{20} + 5 q^{25} + 8 q^{26} - 8 q^{29} + 2 q^{31} + 8 q^{34} - 49 q^{36} - 2 q^{39} - 15 q^{44} + q^{45} - 2 q^{51} - 21 q^{55} - 12 q^{56} - 18 q^{59} + 4 q^{60} - 33 q^{64} + 4 q^{65} - 12 q^{70} - 14 q^{71} + 4 q^{79} - 15 q^{80} + 3 q^{81} - 8 q^{85} - 16 q^{86} + 2 q^{89} - 29 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2695))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2695.1.d \(\chi_{2695}(736, \cdot)\) None 0 1
2695.1.e \(\chi_{2695}(1959, \cdot)\) None 0 1
2695.1.f \(\chi_{2695}(881, \cdot)\) None 0 1
2695.1.g \(\chi_{2695}(1814, \cdot)\) 2695.1.g.a 1 1
2695.1.g.b 1
2695.1.g.c 1
2695.1.g.d 1
2695.1.g.e 1
2695.1.g.f 2
2695.1.g.g 2
2695.1.g.h 2
2695.1.g.i 4
2695.1.l \(\chi_{2695}(538, \cdot)\) 2695.1.l.a 8 2
2695.1.l.b 8
2695.1.m \(\chi_{2695}(1618, \cdot)\) None 0 2
2695.1.p \(\chi_{2695}(166, \cdot)\) None 0 2
2695.1.q \(\chi_{2695}(2419, \cdot)\) 2695.1.q.a 2 2
2695.1.q.b 2
2695.1.q.c 2
2695.1.q.d 2
2695.1.q.e 4
2695.1.q.f 4
2695.1.q.g 8
2695.1.r \(\chi_{2695}(1341, \cdot)\) None 0 2
2695.1.s \(\chi_{2695}(1244, \cdot)\) None 0 2
2695.1.x \(\chi_{2695}(589, \cdot)\) 2695.1.x.a 8 4
2695.1.y \(\chi_{2695}(146, \cdot)\) None 0 4
2695.1.z \(\chi_{2695}(489, \cdot)\) None 0 4
2695.1.ba \(\chi_{2695}(491, \cdot)\) None 0 4
2695.1.bf \(\chi_{2695}(67, \cdot)\) None 0 4
2695.1.bg \(\chi_{2695}(362, \cdot)\) 2695.1.bg.a 16 4
2695.1.bg.b 16
2695.1.bi \(\chi_{2695}(274, \cdot)\) 2695.1.bi.a 6 6
2695.1.bi.b 6
2695.1.bi.c 12
2695.1.bj \(\chi_{2695}(111, \cdot)\) None 0 6
2695.1.bk \(\chi_{2695}(34, \cdot)\) None 0 6
2695.1.bl \(\chi_{2695}(351, \cdot)\) None 0 6
2695.1.bp \(\chi_{2695}(148, \cdot)\) None 0 8
2695.1.bq \(\chi_{2695}(293, \cdot)\) None 0 8
2695.1.bu \(\chi_{2695}(78, \cdot)\) None 0 12
2695.1.bv \(\chi_{2695}(153, \cdot)\) None 0 12
2695.1.ca \(\chi_{2695}(509, \cdot)\) 2695.1.ca.a 8 8
2695.1.ca.b 8
2695.1.cb \(\chi_{2695}(116, \cdot)\) None 0 8
2695.1.cc \(\chi_{2695}(79, \cdot)\) 2695.1.cc.a 16 8
2695.1.cd \(\chi_{2695}(31, \cdot)\) None 0 8
2695.1.ci \(\chi_{2695}(89, \cdot)\) None 0 12
2695.1.cj \(\chi_{2695}(186, \cdot)\) None 0 12
2695.1.ck \(\chi_{2695}(109, \cdot)\) 2695.1.ck.a 12 12
2695.1.ck.b 12
2695.1.ck.c 24
2695.1.cl \(\chi_{2695}(551, \cdot)\) None 0 12
2695.1.cn \(\chi_{2695}(68, \cdot)\) None 0 16
2695.1.co \(\chi_{2695}(312, \cdot)\) None 0 16
2695.1.ct \(\chi_{2695}(106, \cdot)\) None 0 24
2695.1.cu \(\chi_{2695}(69, \cdot)\) None 0 24
2695.1.cv \(\chi_{2695}(181, \cdot)\) None 0 24
2695.1.cw \(\chi_{2695}(29, \cdot)\) None 0 24
2695.1.cy \(\chi_{2695}(87, \cdot)\) None 0 24
2695.1.cz \(\chi_{2695}(23, \cdot)\) None 0 24
2695.1.df \(\chi_{2695}(13, \cdot)\) None 0 48
2695.1.dg \(\chi_{2695}(92, \cdot)\) None 0 48
2695.1.di \(\chi_{2695}(26, \cdot)\) None 0 48
2695.1.dj \(\chi_{2695}(39, \cdot)\) None 0 48
2695.1.dk \(\chi_{2695}(46, \cdot)\) None 0 48
2695.1.dl \(\chi_{2695}(59, \cdot)\) None 0 48
2695.1.dq \(\chi_{2695}(37, \cdot)\) None 0 96
2695.1.dr \(\chi_{2695}(17, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2695))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2695)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2695))\)\(^{\oplus 1}\)