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Properties

Label 3009.2.w
Level $3009$
Weight $2$
Character orbit 3009.w
Rep. character $\chi_{3009}(188,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $8960$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.w (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 10192 8960 1232
Cusp forms 9968 8960 1008
Eisenstein series 224 0 224

Trace form

\( 8960 q + 4 q^{3} - 320 q^{4} + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 8960 q + 4 q^{3} - 320 q^{4} + 8 q^{7} - 4 q^{9} + 28 q^{12} + 4 q^{15} - 304 q^{16} + 8 q^{22} + 272 q^{25} + 40 q^{27} + 24 q^{28} - 28 q^{36} - 74 q^{45} - 272 q^{48} - 344 q^{49} - 222 q^{57} + 80 q^{60} - 266 q^{63} - 408 q^{64} - 88 q^{66} - 348 q^{72} - 78 q^{75} + 136 q^{76} + 28 q^{78} - 64 q^{79} - 36 q^{81} + 128 q^{84} + 64 q^{87} - 96 q^{88} + 120 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into newform subspaces

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

\( S_{2}^{\mathrm{old}}(3009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)