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Properties

Label 625.4
Level 625
Weight 4
Dimension 42816
Nonzero newspaces 8
Sturm bound 125000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 625 = 5^{4} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(125000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(625))\).

Total New Old
Modular forms 47425 43584 3841
Cusp forms 46325 42816 3509
Eisenstein series 1100 768 332

Trace form

\( 42816 q - 160 q^{2} - 160 q^{3} - 160 q^{4} - 200 q^{5} - 288 q^{6} - 160 q^{7} - 160 q^{8} - 160 q^{9} + O(q^{10}) \) \( 42816 q - 160 q^{2} - 160 q^{3} - 160 q^{4} - 200 q^{5} - 288 q^{6} - 160 q^{7} - 160 q^{8} - 160 q^{9} - 200 q^{10} - 288 q^{11} - 160 q^{12} - 160 q^{13} - 160 q^{14} - 200 q^{15} - 544 q^{16} - 480 q^{17} - 610 q^{18} - 280 q^{19} - 200 q^{20} - 48 q^{21} + 560 q^{22} + 280 q^{23} + 1270 q^{24} - 200 q^{25} + 22 q^{26} + 380 q^{27} + 560 q^{28} - 80 q^{29} - 200 q^{30} - 648 q^{31} - 1280 q^{32} - 1120 q^{33} - 1810 q^{34} - 200 q^{35} - 1664 q^{36} - 695 q^{37} - 2650 q^{38} - 2600 q^{39} - 200 q^{40} - 748 q^{41} - 860 q^{42} + 120 q^{43} + 1170 q^{44} - 200 q^{45} + 1932 q^{46} + 1560 q^{47} + 5870 q^{48} + 2035 q^{49} - 200 q^{50} + 2402 q^{51} + 3630 q^{52} + 1505 q^{53} + 3610 q^{54} - 200 q^{55} - 380 q^{56} - 720 q^{57} - 1770 q^{58} - 3460 q^{59} - 200 q^{60} - 4108 q^{61} - 10430 q^{62} - 8380 q^{63} - 7870 q^{64} - 200 q^{65} - 1896 q^{66} + 560 q^{67} + 3680 q^{68} + 2920 q^{69} - 200 q^{70} + 2192 q^{71} + 9090 q^{72} + 2720 q^{73} + 7230 q^{74} - 200 q^{75} + 4830 q^{76} + 5280 q^{77} + 5770 q^{78} + 2000 q^{79} - 200 q^{80} - 1924 q^{81} - 7000 q^{82} - 6940 q^{83} - 13360 q^{84} - 200 q^{85} - 8748 q^{86} - 8820 q^{87} - 12760 q^{88} - 7785 q^{89} - 200 q^{90} - 2088 q^{91} - 5140 q^{92} + 4000 q^{93} + 10880 q^{94} - 200 q^{95} + 10652 q^{96} + 12860 q^{97} + 13340 q^{98} + 11710 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(625))\)

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
625.4.a \(\chi_{625}(1, \cdot)\) 625.4.a.a 10 1
625.4.a.b 10
625.4.a.c 14
625.4.a.d 14
625.4.a.e 20
625.4.a.f 20
625.4.a.g 24
625.4.b \(\chi_{625}(624, \cdot)\) n/a 112 1
625.4.d \(\chi_{625}(126, \cdot)\) n/a 456 4
625.4.e \(\chi_{625}(124, \cdot)\) n/a 456 4
625.4.g \(\chi_{625}(26, \cdot)\) n/a 2180 20
625.4.h \(\chi_{625}(24, \cdot)\) n/a 2200 20
625.4.j \(\chi_{625}(6, \cdot)\) n/a 18700 100
625.4.k \(\chi_{625}(4, \cdot)\) n/a 18600 100

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(625))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(625)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)