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Properties

Label 3040.2.dt
Level $3040$
Weight $2$
Character orbit 3040.dt
Rep. character $\chi_{3040}(79,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
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.dt (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2976 744 2232
Cusp forms 2784 696 2088
Eisenstein series 192 48 144

Trace form

\( 696 q - 24 q^{9} + O(q^{10}) \) \( 696 q - 24 q^{9} + 12 q^{11} + 24 q^{19} - 12 q^{25} - 18 q^{35} - 24 q^{41} - 288 q^{49} + 24 q^{59} - 18 q^{65} + 12 q^{81} - 24 q^{89} - 60 q^{91} - 84 q^{99} + O(q^{100}) \)

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

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