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Properties

Label 1250.2
Level 1250
Weight 2
Dimension 14400
Nonzero newspaces 8
Sturm bound 187500
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1250 = 2 \cdot 5^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(187500\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1250))\).

Total New Old
Modular forms 47975 14400 33575
Cusp forms 45776 14400 31376
Eisenstein series 2199 0 2199

Trace form

\( 14400 q + O(q^{10}) \) \( 14400 q + 20 q^{17} + 25 q^{18} + 40 q^{19} + 40 q^{21} + 40 q^{22} + 40 q^{23} + 20 q^{24} + 20 q^{26} + 60 q^{27} + 20 q^{28} + 40 q^{29} + 40 q^{31} + 5 q^{32} + 40 q^{33} + 25 q^{34} + 5 q^{37} + 40 q^{39} + 20 q^{41} + 40 q^{43} + 40 q^{47} + 45 q^{49} + 60 q^{51} + 45 q^{53} + 80 q^{57} + 60 q^{59} + 60 q^{61} + 60 q^{62} + 140 q^{63} + 60 q^{66} + 80 q^{67} + 60 q^{68} + 140 q^{69} + 80 q^{71} + 80 q^{73} + 100 q^{74} + 40 q^{76} + 160 q^{77} + 100 q^{78} + 80 q^{79} + 80 q^{81} + 80 q^{82} + 160 q^{83} + 60 q^{84} + 60 q^{86} + 140 q^{87} + 105 q^{89} + 80 q^{91} + 20 q^{92} + 60 q^{93} + 20 q^{97} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1250))\)

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
1250.2.a \(\chi_{1250}(1, \cdot)\) 1250.2.a.a 2 1
1250.2.a.b 2
1250.2.a.c 2
1250.2.a.d 2
1250.2.a.e 4
1250.2.a.f 4
1250.2.a.g 4
1250.2.a.h 4
1250.2.a.i 4
1250.2.a.j 4
1250.2.a.k 4
1250.2.a.l 4
1250.2.b \(\chi_{1250}(1249, \cdot)\) 1250.2.b.a 4 1
1250.2.b.b 4
1250.2.b.c 8
1250.2.b.d 8
1250.2.b.e 8
1250.2.b.f 8
1250.2.d \(\chi_{1250}(251, \cdot)\) n/a 160 4
1250.2.e \(\chi_{1250}(249, \cdot)\) n/a 160 4
1250.2.g \(\chi_{1250}(51, \cdot)\) n/a 740 20
1250.2.h \(\chi_{1250}(49, \cdot)\) n/a 760 20
1250.2.j \(\chi_{1250}(11, \cdot)\) n/a 6300 100
1250.2.k \(\chi_{1250}(9, \cdot)\) n/a 6200 100

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1250))\) into lower level spaces

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