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Properties

Label 3360.2.if
Level $3360$
Weight $2$
Character orbit 3360.if
Rep. character $\chi_{3360}(67,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $3072$
Sturm bound $1536$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3360.if (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1120 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).

Total New Old
Modular forms 6208 3072 3136
Cusp forms 6080 3072 3008
Eisenstein series 128 0 128

Trace form

\( 3072 q - 48 q^{8} + O(q^{10}) \) \( 3072 q - 48 q^{8} + 24 q^{10} - 48 q^{35} + 40 q^{42} - 32 q^{44} + 64 q^{48} + 72 q^{52} + 32 q^{58} - 288 q^{62} - 192 q^{64} - 48 q^{66} - 48 q^{67} + 72 q^{70} + 128 q^{71} + 96 q^{78} - 176 q^{80} - 40 q^{82} - 88 q^{88} + 144 q^{92} - 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)