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Properties

Label 2500.4
Level 2500
Weight 4
Dimension 301632
Nonzero newspaces 12
Sturm bound 1500000
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2500 = 2^{2} \cdot 5^{4} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1500000\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2500))\).

Total New Old
Modular forms 565250 303168 262082
Cusp forms 559750 301632 258118
Eisenstein series 5500 1536 3964

Trace form

\( 301632 q - 160 q^{2} - 160 q^{4} - 400 q^{5} - 288 q^{6} - 160 q^{8} - 320 q^{9} + O(q^{10}) \) \( 301632 q - 160 q^{2} - 160 q^{4} - 400 q^{5} - 288 q^{6} - 160 q^{8} - 320 q^{9} - 200 q^{10} - 160 q^{12} - 320 q^{13} - 160 q^{14} - 288 q^{16} - 640 q^{17} - 160 q^{18} - 120 q^{19} - 200 q^{20} - 336 q^{21} - 160 q^{22} + 440 q^{23} - 150 q^{24} - 400 q^{25} - 418 q^{26} + 540 q^{27} - 160 q^{28} - 240 q^{29} - 200 q^{30} - 360 q^{31} - 160 q^{32} - 1280 q^{33} - 160 q^{34} + 224 q^{36} + 215 q^{37} + 2330 q^{38} + 2440 q^{39} - 200 q^{40} - 116 q^{41} + 540 q^{42} - 280 q^{43} - 1490 q^{44} - 400 q^{45} - 2508 q^{46} - 1720 q^{47} - 6270 q^{48} - 2505 q^{49} - 200 q^{50} - 2820 q^{51} - 4030 q^{52} - 1985 q^{53} - 3930 q^{54} - 708 q^{56} + 240 q^{57} + 1450 q^{58} - 20 q^{59} - 200 q^{60} - 1076 q^{61} + 5190 q^{62} + 2420 q^{63} + 4670 q^{64} - 400 q^{65} + 1440 q^{66} + 720 q^{67} - 160 q^{68} + 2760 q^{69} - 200 q^{70} + 2480 q^{71} - 430 q^{72} + 2560 q^{73} - 150 q^{74} - 930 q^{76} + 5120 q^{77} + 110 q^{78} + 2160 q^{79} - 200 q^{80} + 6536 q^{81} - 8440 q^{82} + 3600 q^{83} - 11440 q^{84} - 400 q^{85} - 5268 q^{86} - 1820 q^{87} - 4120 q^{88} - 5635 q^{89} - 200 q^{90} - 5040 q^{91} + 4140 q^{92} - 9840 q^{93} + 10880 q^{94} + 8412 q^{96} - 20780 q^{97} + 13500 q^{98} - 5940 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2500))\)

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
2500.4.a \(\chi_{2500}(1, \cdot)\) 2500.4.a.a 10 1
2500.4.a.b 10
2500.4.a.c 14
2500.4.a.d 14
2500.4.a.e 20
2500.4.a.f 20
2500.4.a.g 32
2500.4.c \(\chi_{2500}(1249, \cdot)\) n/a 120 1
2500.4.e \(\chi_{2500}(443, \cdot)\) n/a 1408 2
2500.4.g \(\chi_{2500}(501, \cdot)\) n/a 480 4
2500.4.i \(\chi_{2500}(249, \cdot)\) n/a 480 4
2500.4.l \(\chi_{2500}(307, \cdot)\) n/a 5664 8
2500.4.m \(\chi_{2500}(101, \cdot)\) n/a 2260 20
2500.4.o \(\chi_{2500}(49, \cdot)\) n/a 2240 20
2500.4.r \(\chi_{2500}(7, \cdot)\) n/a 26760 40
2500.4.s \(\chi_{2500}(21, \cdot)\) n/a 18700 100
2500.4.u \(\chi_{2500}(9, \cdot)\) n/a 18800 100
2500.4.x \(\chi_{2500}(3, \cdot)\) n/a 224600 200

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2500))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2500)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2500))\)\(^{\oplus 1}\)