Properties

Label 3004.2
Level 3004
Weight 2
Dimension 163750
Nonzero newspaces 16
Sturm bound 1128000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(1128000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3004))\).

Total New Old
Modular forms 283875 165250 118625
Cusp forms 280126 163750 116376
Eisenstein series 3749 1500 2249

Trace form

\( 163750q - 375q^{2} - 375q^{4} - 750q^{5} - 375q^{6} - 375q^{8} - 750q^{9} + O(q^{10}) \) \( 163750q - 375q^{2} - 375q^{4} - 750q^{5} - 375q^{6} - 375q^{8} - 750q^{9} - 375q^{10} - 375q^{12} - 750q^{13} - 375q^{14} - 375q^{16} - 750q^{17} - 375q^{18} - 375q^{20} - 750q^{21} - 375q^{22} - 375q^{24} - 750q^{25} - 375q^{26} - 375q^{28} - 750q^{29} - 375q^{30} - 375q^{32} - 750q^{33} - 375q^{34} - 375q^{36} - 750q^{37} - 375q^{38} - 375q^{40} - 750q^{41} - 375q^{42} - 375q^{44} - 750q^{45} - 375q^{46} - 375q^{48} - 750q^{49} - 375q^{50} - 375q^{52} - 750q^{53} - 375q^{54} - 375q^{56} - 750q^{57} - 375q^{58} - 375q^{60} - 750q^{61} - 375q^{62} - 375q^{64} - 750q^{65} - 375q^{66} - 375q^{68} - 750q^{69} - 375q^{70} - 375q^{72} - 750q^{73} - 375q^{74} - 375q^{76} - 750q^{77} - 375q^{78} - 375q^{80} - 750q^{81} - 375q^{82} - 375q^{84} - 750q^{85} - 375q^{86} - 375q^{88} - 750q^{89} - 375q^{90} - 375q^{92} - 750q^{93} - 375q^{94} - 375q^{96} - 750q^{97} - 375q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3004))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
3004.2.a \(\chi_{3004}(1, \cdot)\) 3004.2.a.a 1 1
3004.2.a.b 2
3004.2.a.c 28
3004.2.a.d 31
3004.2.d \(\chi_{3004}(3003, \cdot)\) n/a 374 1
3004.2.e \(\chi_{3004}(1429, \cdot)\) n/a 126 2
3004.2.f \(\chi_{3004}(569, \cdot)\) n/a 248 4
3004.2.g \(\chi_{3004}(679, \cdot)\) n/a 748 2
3004.2.j \(\chi_{3004}(291, \cdot)\) n/a 1496 4
3004.2.m \(\chi_{3004}(437, \cdot)\) n/a 504 8
3004.2.n \(\chi_{3004}(53, \cdot)\) n/a 1240 20
3004.2.q \(\chi_{3004}(583, \cdot)\) n/a 2992 8
3004.2.r \(\chi_{3004}(195, \cdot)\) n/a 7480 20
3004.2.u \(\chi_{3004}(61, \cdot)\) n/a 2520 40
3004.2.v \(\chi_{3004}(45, \cdot)\) n/a 6200 100
3004.2.y \(\chi_{3004}(11, \cdot)\) n/a 14960 40
3004.2.ba \(\chi_{3004}(7, \cdot)\) n/a 37400 100
3004.2.bc \(\chi_{3004}(5, \cdot)\) n/a 12600 200
3004.2.be \(\chi_{3004}(3, \cdot)\) n/a 74800 200

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(751))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1502))\)\(^{\oplus 2}\)