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Properties

Label 3360.2.im
Level $3360$
Weight $2$
Character orbit 3360.im
Rep. character $\chi_{3360}(179,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $6080$
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.im (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3360 \)
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 6208 0
Cusp forms 6080 6080 0
Eisenstein series 128 128 0

Trace form

\( 6080 q - 16 q^{4} - 32 q^{6} - 8 q^{9} + O(q^{10}) \) \( 6080 q - 16 q^{4} - 32 q^{6} - 8 q^{9} - 8 q^{10} - 32 q^{15} - 16 q^{16} - 16 q^{19} - 16 q^{21} - 8 q^{24} - 8 q^{25} - 52 q^{30} - 128 q^{34} - 192 q^{36} - 8 q^{39} + 56 q^{40} - 4 q^{45} - 16 q^{46} - 56 q^{51} - 8 q^{54} - 32 q^{55} - 20 q^{60} - 16 q^{61} + 32 q^{64} + 24 q^{66} - 32 q^{69} - 16 q^{70} - 4 q^{75} - 64 q^{76} - 32 q^{79} + 80 q^{84} - 112 q^{85} - 16 q^{90} - 32 q^{91} + 48 q^{94} - 8 q^{96} - 32 q^{99} + O(q^{100}) \)

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.