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Properties

Label 3009.2.t
Level $3009$
Weight $2$
Character orbit 3009.t
Rep. character $\chi_{3009}(58,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1440$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.t (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2912 1440 1472
Cusp forms 2848 1440 1408
Eisenstein series 64 0 64

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q + 32 q^{17} - 32 q^{19} - 64 q^{22} + 128 q^{26} - 128 q^{35} + 64 q^{46} - 64 q^{49} + 64 q^{59} - 192 q^{64} + 64 q^{71} - 192 q^{74} - 64 q^{75} + 128 q^{78} - 64 q^{79} - 224 q^{80} + 96 q^{85} + 96 q^{87} - 128 q^{88} - 64 q^{94} - 128 q^{95} + O(q^{100}) \)

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

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