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Properties

Label 3040.2.dd
Level $3040$
Weight $2$
Character orbit 3040.dd
Rep. character $\chi_{3040}(753,\cdot)$
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.dd (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

\( 464 q + 16 q^{7} + O(q^{10}) \) \( 464 q + 16 q^{7} + 12 q^{15} - 4 q^{17} + 4 q^{23} - 4 q^{25} + 24 q^{33} - 24 q^{41} + 28 q^{47} - 16 q^{55} - 20 q^{57} - 48 q^{63} + 24 q^{71} - 4 q^{73} + 160 q^{81} + 152 q^{87} - 36 q^{95} - 12 q^{97} + O(q^{100}) \)

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

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