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Properties

Label 3009.2.v
Level $3009$
Weight $2$
Character orbit 3009.v
Rep. character $\chi_{3009}(50,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $9968$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.v (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3009 \)
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 10192 0
Cusp forms 9968 9968 0
Eisenstein series 224 224 0

Trace form

\( 9968 q - 460 q^{4} - 42 q^{9} + O(q^{10}) \) \( 9968 q - 460 q^{4} - 42 q^{9} - 116 q^{13} - 48 q^{15} - 436 q^{16} - 58 q^{18} - 84 q^{19} - 48 q^{21} - 448 q^{25} - 58 q^{30} - 58 q^{33} - 58 q^{34} - 2 q^{36} - 58 q^{42} - 116 q^{43} + 192 q^{49} - 181 q^{51} - 116 q^{52} - 116 q^{55} + 692 q^{60} - 388 q^{64} - 464 q^{66} - 116 q^{67} + 174 q^{69} - 116 q^{70} - 58 q^{72} - 20 q^{76} - 42 q^{81} - 42 q^{84} - 78 q^{85} + 4 q^{87} - 58 q^{93} - 172 q^{94} + O(q^{100}) \)

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.