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Properties

Label 3009.2.x
Level $3009$
Weight $2$
Character orbit 3009.x
Rep. character $\chi_{3009}(16,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $5040$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.x (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
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 5040 5152
Cusp forms 9968 5040 4928
Eisenstein series 224 0 224

Trace form

\( 5040 q - 180 q^{4} + 180 q^{9} + O(q^{10}) \) \( 5040 q - 180 q^{4} + 180 q^{9} - 16 q^{13} - 148 q^{16} - 8 q^{17} - 8 q^{19} + 180 q^{25} + 8 q^{26} - 40 q^{30} - 40 q^{32} - 8 q^{33} - 16 q^{34} + 180 q^{36} + 96 q^{38} - 8 q^{42} + 16 q^{43} - 84 q^{47} - 44 q^{49} + 160 q^{50} + 16 q^{51} + 440 q^{52} - 68 q^{53} - 16 q^{55} + 24 q^{59} - 1092 q^{64} + 16 q^{66} + 100 q^{67} - 224 q^{68} + 16 q^{69} - 168 q^{70} - 64 q^{76} - 56 q^{77} - 180 q^{81} + 56 q^{83} + 80 q^{84} - 36 q^{85} + 80 q^{86} - 24 q^{87} - 16 q^{89} - 8 q^{93} - 120 q^{94} - 112 q^{98} + O(q^{100}) \)

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

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