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Properties

Label 1250.4
Level 1250
Weight 4
Dimension 43200
Nonzero newspaces 8
Sturm bound 375000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1250 = 2 \cdot 5^{4} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(375000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1250))\).

Total New Old
Modular forms 141725 43200 98525
Cusp forms 139525 43200 96325
Eisenstein series 2200 0 2200

Trace form

\( 43200 q + O(q^{10}) \) \( 43200 q + 640 q^{17} + 450 q^{18} + 240 q^{19} - 480 q^{21} - 720 q^{22} - 880 q^{23} - 480 q^{24} - 440 q^{26} - 1080 q^{27} - 240 q^{28} - 160 q^{29} + 720 q^{31} + 160 q^{32} + 1920 q^{33} + 1650 q^{34} + 535 q^{37} + 2440 q^{39} + 460 q^{41} - 280 q^{43} - 1720 q^{47} - 2205 q^{49} - 2820 q^{51} - 1665 q^{53} + 560 q^{57} + 4960 q^{59} + 5980 q^{61} + 4920 q^{62} + 11120 q^{63} - 120 q^{66} - 1440 q^{67} - 1920 q^{68} - 6160 q^{69} - 4960 q^{71} - 5760 q^{73} - 7400 q^{74} - 2880 q^{76} - 10880 q^{77} - 6200 q^{78} - 4320 q^{79} - 2560 q^{81} - 1440 q^{82} + 3180 q^{83} + 960 q^{84} + 3480 q^{86} + 10480 q^{87} + 13655 q^{89} + 6840 q^{91} + 4640 q^{92} + 3080 q^{93} - 1860 q^{97} - 5940 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1250))\)

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
1250.4.a \(\chi_{1250}(1, \cdot)\) 1250.4.a.a 4 1
1250.4.a.b 4
1250.4.a.c 6
1250.4.a.d 6
1250.4.a.e 6
1250.4.a.f 6
1250.4.a.g 8
1250.4.a.h 8
1250.4.a.i 8
1250.4.a.j 8
1250.4.a.k 12
1250.4.a.l 12
1250.4.a.m 16
1250.4.a.n 16
1250.4.b \(\chi_{1250}(1249, \cdot)\) n/a 120 1
1250.4.d \(\chi_{1250}(251, \cdot)\) n/a 480 4
1250.4.e \(\chi_{1250}(249, \cdot)\) n/a 480 4
1250.4.g \(\chi_{1250}(51, \cdot)\) n/a 2260 20
1250.4.h \(\chi_{1250}(49, \cdot)\) n/a 2240 20
1250.4.j \(\chi_{1250}(11, \cdot)\) n/a 18700 100
1250.4.k \(\chi_{1250}(9, \cdot)\) n/a 18800 100

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1250))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1250)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1250))\)\(^{\oplus 1}\)