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Properties

Label 3360.2.ew
Level $3360$
Weight $2$
Character orbit 3360.ew
Rep. character $\chi_{3360}(83,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $3040$
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.ew (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3360 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1536\)

Dimensions

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

Total New Old
Modular forms 3104 3104 0
Cusp forms 3040 3040 0
Eisenstein series 64 64 0

Trace form

\( 3040 q - 16 q^{7} + O(q^{10}) \) \( 3040 q - 16 q^{7} - 16 q^{15} - 32 q^{16} + 8 q^{18} - 8 q^{21} - 16 q^{22} - 16 q^{25} - 40 q^{28} + 32 q^{30} - 16 q^{36} - 16 q^{37} + 20 q^{42} - 16 q^{43} - 32 q^{46} - 16 q^{51} + 48 q^{58} + 24 q^{60} - 56 q^{63} - 16 q^{67} + 48 q^{70} - 72 q^{72} - 144 q^{78} + 56 q^{84} - 16 q^{85} - 16 q^{88} - 16 q^{91} - 32 q^{93} + O(q^{100}) \)

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.