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Properties

Label 3120.2.kf
Level $3120$
Weight $2$
Character orbit 3120.kf
Rep. character $\chi_{3120}(227,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2656$
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.kf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3120 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2720 2720 0
Cusp forms 2656 2656 0
Eisenstein series 64 64 0

Trace form

\( 2656 q - 8 q^{6} - 24 q^{7} + O(q^{10}) \) \( 2656 q - 8 q^{6} - 24 q^{7} - 20 q^{10} - 16 q^{13} + 12 q^{15} - 8 q^{16} - 16 q^{21} - 12 q^{22} + 28 q^{24} - 12 q^{28} - 8 q^{30} - 4 q^{33} - 16 q^{34} - 28 q^{36} - 16 q^{37} - 56 q^{40} + 4 q^{42} - 24 q^{43} + 8 q^{45} - 16 q^{46} + 64 q^{48} + 1232 q^{49} - 44 q^{52} - 8 q^{55} + 28 q^{58} - 8 q^{61} - 16 q^{66} - 16 q^{67} - 32 q^{70} - 54 q^{72} - 24 q^{75} + 16 q^{76} - 40 q^{78} - 8 q^{81} - 4 q^{82} - 4 q^{84} + 56 q^{85} - 4 q^{87} - 172 q^{88} - 16 q^{91} - 20 q^{93} + 48 q^{94} + 80 q^{96} - 8 q^{97} + O(q^{100}) \)

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.