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Properties

Label 3020.2.g
Level $3020$
Weight $2$
Character orbit 3020.g
Rep. character $\chi_{3020}(1811,\cdot)$
Character field $\Q$
Dimension $304$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 3020 = 2^{2} \cdot 5 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3020.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 604 \)
Character field: \(\Q\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3020, [\chi])\).

Total New Old
Modular forms 460 304 156
Cusp forms 452 304 148
Eisenstein series 8 0 8

Trace form

\( 304 q + 4 q^{2} + 8 q^{4} - 8 q^{8} + 304 q^{9} + O(q^{10}) \) \( 304 q + 4 q^{2} + 8 q^{4} - 8 q^{8} + 304 q^{9} + 4 q^{10} + 24 q^{16} + 8 q^{18} - 16 q^{21} - 8 q^{22} + 304 q^{25} - 32 q^{29} + 4 q^{32} - 44 q^{34} + 8 q^{36} - 16 q^{37} + 40 q^{38} + 16 q^{40} - 64 q^{42} + 352 q^{49} + 4 q^{50} + 12 q^{58} - 12 q^{62} + 80 q^{64} + 76 q^{68} - 32 q^{69} - 68 q^{72} + 16 q^{74} + 36 q^{76} + 304 q^{81} - 60 q^{84} - 32 q^{85} - 12 q^{86} + 12 q^{88} - 20 q^{90} + 24 q^{94} - 48 q^{97} - 4 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3020, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3020, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(604, [\chi])\)\(^{\oplus 2}\)