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Properties

Label 2904.1
Level 2904
Weight 1
Dimension 292
Nonzero newspaces 8
Newform subspaces 30
Sturm bound 464640
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 30 \)
Sturm bound: \(464640\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2904))\).

Total New Old
Modular forms 4480 854 3626
Cusp forms 640 292 348
Eisenstein series 3840 562 3278

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 292 0 0 0

Trace form

\( 292 q + 2 q^{4} + 12 q^{6} + 4 q^{7} + 2 q^{9} + O(q^{10}) \) \( 292 q + 2 q^{4} + 12 q^{6} + 4 q^{7} + 2 q^{9} + 4 q^{10} - 20 q^{12} - 16 q^{15} + 2 q^{16} + 10 q^{18} + 20 q^{19} - 8 q^{24} + 6 q^{25} - 16 q^{28} - 16 q^{31} + 5 q^{33} - 8 q^{36} - 16 q^{40} - 16 q^{42} + 6 q^{49} - 10 q^{51} - 18 q^{54} + 10 q^{57} - 16 q^{58} + 4 q^{60} + 4 q^{63} + 2 q^{64} - 12 q^{70} - 16 q^{73} - 10 q^{75} + 4 q^{79} + 2 q^{81} - 20 q^{82} + 4 q^{87} + 4 q^{90} + 2 q^{96} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2904))\)

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
2904.1.c \(\chi_{2904}(2179, \cdot)\) None 0 1
2904.1.e \(\chi_{2904}(1693, \cdot)\) None 0 1
2904.1.g \(\chi_{2904}(2903, \cdot)\) None 0 1
2904.1.i \(\chi_{2904}(1937, \cdot)\) None 0 1
2904.1.j \(\chi_{2904}(241, \cdot)\) None 0 1
2904.1.l \(\chi_{2904}(727, \cdot)\) None 0 1
2904.1.n \(\chi_{2904}(485, \cdot)\) 2904.1.n.a 2 1
2904.1.n.b 2
2904.1.n.c 2
2904.1.n.d 2
2904.1.p \(\chi_{2904}(1451, \cdot)\) 2904.1.p.a 4 1
2904.1.p.b 4
2904.1.p.c 4
2904.1.r \(\chi_{2904}(1667, \cdot)\) 2904.1.r.a 4 4
2904.1.r.b 4
2904.1.r.c 4
2904.1.r.d 4
2904.1.r.e 4
2904.1.r.f 4
2904.1.r.g 4
2904.1.r.h 4
2904.1.r.i 16
2904.1.t \(\chi_{2904}(245, \cdot)\) 2904.1.t.a 4 4
2904.1.t.b 4
2904.1.t.c 4
2904.1.t.d 4
2904.1.t.e 4
2904.1.t.f 4
2904.1.v \(\chi_{2904}(487, \cdot)\) None 0 4
2904.1.x \(\chi_{2904}(457, \cdot)\) None 0 4
2904.1.y \(\chi_{2904}(977, \cdot)\) None 0 4
2904.1.ba \(\chi_{2904}(215, \cdot)\) None 0 4
2904.1.bc \(\chi_{2904}(1909, \cdot)\) None 0 4
2904.1.be \(\chi_{2904}(1219, \cdot)\) None 0 4
2904.1.bh \(\chi_{2904}(131, \cdot)\) 2904.1.bh.a 10 10
2904.1.bh.b 10
2904.1.bj \(\chi_{2904}(221, \cdot)\) 2904.1.bj.a 10 10
2904.1.bj.b 10
2904.1.bl \(\chi_{2904}(199, \cdot)\) None 0 10
2904.1.bn \(\chi_{2904}(505, \cdot)\) None 0 10
2904.1.bo \(\chi_{2904}(89, \cdot)\) None 0 10
2904.1.bq \(\chi_{2904}(263, \cdot)\) None 0 10
2904.1.bs \(\chi_{2904}(109, \cdot)\) None 0 10
2904.1.bu \(\chi_{2904}(67, \cdot)\) None 0 10
2904.1.by \(\chi_{2904}(91, \cdot)\) None 0 40
2904.1.ca \(\chi_{2904}(13, \cdot)\) None 0 40
2904.1.cc \(\chi_{2904}(95, \cdot)\) None 0 40
2904.1.ce \(\chi_{2904}(113, \cdot)\) None 0 40
2904.1.cf \(\chi_{2904}(73, \cdot)\) None 0 40
2904.1.ch \(\chi_{2904}(31, \cdot)\) None 0 40
2904.1.cj \(\chi_{2904}(5, \cdot)\) 2904.1.cj.a 40 40
2904.1.cj.b 40
2904.1.cl \(\chi_{2904}(35, \cdot)\) 2904.1.cl.a 40 40
2904.1.cl.b 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2904))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2904)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1452))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2904))\)\(^{\oplus 1}\)