Properties

Label 3009.2.n
Level 3009
Weight 2
Character orbit n
Rep. character \(\chi_{3009}(178,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 704
Sturm bound 720

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3009.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

Total New Old
Modular forms 1456 704 752
Cusp forms 1424 704 720
Eisenstein series 32 0 32

Trace form

\( 704q + 16q^{5} + 16q^{6} + O(q^{10}) \) \( 704q + 16q^{5} + 16q^{6} - 16q^{11} - 752q^{16} + 32q^{19} - 32q^{20} + 48q^{22} - 16q^{24} + 32q^{25} + 32q^{26} + 16q^{28} - 16q^{29} + 16q^{31} - 80q^{32} + 16q^{33} - 16q^{34} - 16q^{36} + 32q^{37} - 32q^{40} + 16q^{41} - 48q^{42} - 16q^{43} + 16q^{45} + 32q^{46} + 16q^{49} - 64q^{52} + 48q^{53} + 16q^{54} + 112q^{56} + 16q^{60} + 64q^{61} - 32q^{62} - 112q^{65} + 64q^{67} - 80q^{68} - 16q^{69} - 144q^{70} - 128q^{73} - 32q^{74} - 176q^{76} + 160q^{77} + 48q^{78} + 16q^{80} - 64q^{83} - 32q^{85} - 64q^{86} + 80q^{88} - 160q^{92} + 96q^{93} + 16q^{94} + 144q^{95} + 32q^{96} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3009, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 2}\)