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Properties

Label 3009.2.bk
Level $3009$
Weight $2$
Character orbit 3009.bk
Rep. character $\chi_{3009}(10,\cdot)$
Character field $\Q(\zeta_{464})$
Dimension $40320$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.bk (of order \(464\) and degree \(224\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{464})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 81536 40320 41216
Cusp forms 79744 40320 39424
Eisenstein series 1792 0 1792

Trace form

\( 40320 q + O(q^{10}) \) \( 40320 q - 32 q^{17} + 32 q^{19} + 64 q^{22} - 128 q^{26} + 128 q^{35} - 64 q^{46} + 64 q^{49} - 64 q^{59} + 192 q^{64} - 992 q^{71} + 192 q^{74} + 64 q^{75} - 128 q^{78} + 64 q^{79} + 224 q^{80} - 96 q^{85} - 96 q^{87} + 128 q^{88} + 64 q^{94} + 128 q^{95} + O(q^{100}) \)

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

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