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Properties

Label 3040.2.dk
Level $3040$
Weight $2$
Character orbit 3040.dk
Rep. character $\chi_{3040}(463,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $464$
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.dk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1984 496 1488
Cusp forms 1856 464 1392
Eisenstein series 128 32 96

Trace form

\( 464 q + 4 q^{3} + O(q^{10}) \) \( 464 q + 4 q^{3} + 32 q^{11} - 4 q^{17} - 4 q^{25} + 40 q^{27} - 16 q^{33} + 52 q^{35} - 8 q^{41} + 4 q^{43} - 8 q^{51} - 20 q^{57} - 16 q^{65} - 44 q^{67} - 4 q^{73} + 240 q^{75} + 160 q^{81} - 64 q^{83} + 8 q^{91} - 4 q^{97} + O(q^{100}) \)

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

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