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Properties

Label 2464.2.dp
Level $2464$
Weight $2$
Character orbit 2464.dp
Rep. character $\chi_{2464}(47,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $736$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2464 = 2^{5} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2464.dp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 616 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2464, [\chi])\).

Total New Old
Modular forms 3200 800 2400
Cusp forms 2944 736 2208
Eisenstein series 256 64 192

Trace form

\( 736 q + 18 q^{3} - 90 q^{9} + O(q^{10}) \) \( 736 q + 18 q^{3} - 90 q^{9} + 4 q^{11} - 18 q^{17} + 18 q^{19} + 70 q^{25} - 24 q^{33} + 32 q^{35} + 80 q^{43} - 12 q^{49} - 18 q^{51} + 66 q^{59} + 4 q^{65} + 56 q^{67} - 18 q^{73} + 78 q^{75} + 42 q^{81} - 48 q^{89} + 12 q^{91} + 216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2464, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2464, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2464, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)