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Properties

Label 3040.2.ff
Level $3040$
Weight $2$
Character orbit 3040.ff
Rep. character $\chi_{3040}(47,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1392$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3040.ff (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

Total New Old
Modular forms 5952 1488 4464
Cusp forms 5568 1392 4176
Eisenstein series 384 96 288

Trace form

\( 1392 q + 24 q^{3} + O(q^{10}) \) \( 1392 q + 24 q^{3} + 24 q^{11} - 24 q^{17} - 24 q^{25} + 12 q^{27} + 12 q^{33} + 24 q^{35} - 48 q^{41} + 24 q^{43} + 96 q^{51} - 24 q^{57} - 12 q^{65} + 24 q^{67} - 24 q^{73} - 288 q^{75} - 48 q^{81} + 12 q^{83} + 48 q^{91} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1520, [\chi])\)\(^{\oplus 2}\)