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Properties

Label 2401.4
Level 2401
Weight 4
Dimension 675540
Nonzero newspaces 8
Sturm bound 1882384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2401 = 7^{4} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(1882384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2401))\).

Total New Old
Modular forms 708246 679212 29034
Cusp forms 703542 675540 28002
Eisenstein series 4704 3672 1032

Trace form

\( 675540 q - 756 q^{2} - 756 q^{3} - 756 q^{4} - 756 q^{5} - 756 q^{6} - 882 q^{7} - 1404 q^{8} - 756 q^{9} + O(q^{10}) \) \( 675540 q - 756 q^{2} - 756 q^{3} - 756 q^{4} - 756 q^{5} - 756 q^{6} - 882 q^{7} - 1404 q^{8} - 756 q^{9} - 756 q^{10} - 756 q^{11} - 756 q^{12} - 756 q^{13} - 882 q^{14} - 1404 q^{15} - 756 q^{16} - 756 q^{17} - 756 q^{18} - 756 q^{19} - 756 q^{20} - 882 q^{21} - 1404 q^{22} - 756 q^{23} - 756 q^{24} - 756 q^{25} - 756 q^{26} - 756 q^{27} - 882 q^{28} - 1404 q^{29} - 756 q^{30} - 756 q^{31} - 756 q^{32} - 756 q^{33} - 756 q^{34} - 882 q^{35} - 3348 q^{36} - 3108 q^{37} - 3360 q^{38} - 2814 q^{39} - 3780 q^{40} - 1092 q^{41} - 882 q^{42} - 648 q^{43} + 2772 q^{44} + 3024 q^{45} + 4536 q^{46} + 1176 q^{47} + 6615 q^{48} - 882 q^{49} + 1809 q^{50} + 2772 q^{51} + 4788 q^{52} + 420 q^{53} + 1512 q^{54} - 126 q^{55} - 882 q^{56} - 2412 q^{57} - 4284 q^{58} - 3360 q^{59} - 11340 q^{60} - 6048 q^{61} - 6384 q^{62} - 882 q^{63} - 6012 q^{64} - 756 q^{65} - 756 q^{66} - 756 q^{67} - 756 q^{68} - 756 q^{69} - 882 q^{70} - 1404 q^{71} - 756 q^{72} - 756 q^{73} - 756 q^{74} - 756 q^{75} - 756 q^{76} - 882 q^{77} - 5292 q^{78} - 756 q^{79} - 13923 q^{80} - 15456 q^{81} - 15771 q^{82} - 10248 q^{83} - 882 q^{84} - 6360 q^{85} - 5901 q^{86} - 2940 q^{87} + 861 q^{88} + 1344 q^{89} + 15603 q^{90} - 882 q^{91} + 8445 q^{92} + 18648 q^{93} + 15309 q^{94} + 14532 q^{95} + 32991 q^{96} + 7371 q^{97} - 882 q^{98} + 13905 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2401))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2401.4.a \(\chi_{2401}(1, \cdot)\) 2401.4.a.a 33 1
2401.4.a.b 33
2401.4.a.c 39
2401.4.a.d 39
2401.4.a.e 66
2401.4.a.f 78
2401.4.a.g 78
2401.4.a.h 120
2401.4.c \(\chi_{2401}(1047, \cdot)\) n/a 972 2
2401.4.e \(\chi_{2401}(344, \cdot)\) n/a 2934 6
2401.4.g \(\chi_{2401}(18, \cdot)\) n/a 5868 12
2401.4.i \(\chi_{2401}(50, \cdot)\) n/a 20370 42
2401.4.k \(\chi_{2401}(30, \cdot)\) n/a 40740 84
2401.4.m \(\chi_{2401}(8, \cdot)\) n/a 201390 294
2401.4.o \(\chi_{2401}(2, \cdot)\) n/a 402780 588

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2401))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2401)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 2}\)