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Properties

Label 309.5
Level 309
Weight 5
Dimension 10506
Nonzero newspaces 8
Sturm bound 35360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 309 = 3 \cdot 103 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(35360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(309))\).

Total New Old
Modular forms 14348 10706 3642
Cusp forms 13940 10506 3434
Eisenstein series 408 200 208

Trace form

\( 10506 q - 51 q^{3} - 102 q^{4} - 51 q^{6} - 102 q^{7} - 51 q^{9} + O(q^{10}) \) \( 10506 q - 51 q^{3} - 102 q^{4} - 51 q^{6} - 102 q^{7} - 51 q^{9} - 102 q^{10} - 51 q^{12} - 102 q^{13} - 51 q^{15} - 102 q^{16} - 51 q^{18} - 102 q^{19} - 51 q^{21} - 102 q^{22} - 51 q^{24} - 102 q^{25} - 51 q^{27} - 102 q^{28} - 51 q^{30} - 102 q^{31} - 51 q^{33} - 102 q^{34} - 51 q^{36} - 102 q^{37} - 51 q^{39} - 102 q^{40} - 51 q^{42} - 102 q^{43} - 51 q^{45} - 102 q^{46} - 51 q^{48} - 102 q^{49} - 51 q^{51} - 102 q^{52} - 51 q^{54} - 102 q^{55} - 51 q^{57} - 102 q^{58} - 51 q^{60} - 102 q^{61} - 51 q^{63} - 102 q^{64} - 51 q^{66} - 102 q^{67} - 51 q^{69} - 102 q^{70} - 51 q^{72} - 102 q^{73} - 51 q^{75} - 102 q^{76} - 51 q^{78} - 102 q^{79} - 51 q^{81} - 102 q^{82} - 190995 q^{84} - 412794 q^{85} - 274176 q^{86} - 78081 q^{87} - 228582 q^{88} + 23868 q^{89} + 44013 q^{90} + 296480 q^{91} + 342720 q^{92} + 192729 q^{93} + 404634 q^{94} + 302022 q^{95} + 572781 q^{96} + 373388 q^{97} + 587520 q^{98} + 57783 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(309))\)

We only show spaces with odd 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
309.5.b \(\chi_{309}(104, \cdot)\) n/a 136 1
309.5.d \(\chi_{309}(205, \cdot)\) 309.5.d.a 70 1
309.5.f \(\chi_{309}(160, \cdot)\) n/a 138 2
309.5.h \(\chi_{309}(56, \cdot)\) n/a 274 2
309.5.j \(\chi_{309}(10, \cdot)\) n/a 1120 16
309.5.l \(\chi_{309}(8, \cdot)\) n/a 2176 16
309.5.n \(\chi_{309}(2, \cdot)\) n/a 4384 32
309.5.p \(\chi_{309}(40, \cdot)\) n/a 2208 32

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(309))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(309)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 1}\)