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Properties

Label 3120.2.bi
Level $3120$
Weight $2$
Character orbit 3120.bi
Rep. character $\chi_{3120}(1763,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1328$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3120.bi (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3120 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q - 8 q^{3} - 4 q^{6} + O(q^{10}) \) \( 1328 q - 8 q^{3} - 4 q^{6} - 8 q^{10} + 12 q^{15} - 16 q^{16} - 4 q^{24} - 8 q^{27} + 12 q^{30} - 8 q^{33} + 16 q^{34} + 32 q^{36} + 8 q^{37} + 32 q^{40} + 8 q^{42} - 32 q^{43} - 8 q^{46} - 16 q^{48} - 1232 q^{49} - 40 q^{52} + 24 q^{54} - 16 q^{55} - 32 q^{58} + 48 q^{60} - 16 q^{61} - 8 q^{66} - 8 q^{67} - 8 q^{70} + 24 q^{76} + 8 q^{78} - 16 q^{81} - 24 q^{82} + 52 q^{84} + 40 q^{85} - 8 q^{87} + 120 q^{88} - 8 q^{91} - 8 q^{93} + 16 q^{96} - 16 q^{97} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) into newform subspaces

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