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Properties

Label 3120.2.ki
Level $3120$
Weight $2$
Character orbit 3120.ki
Rep. character $\chi_{3120}(419,\cdot)$
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.ki (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

\( 2656 q - 8 q^{4} - 4 q^{6} + O(q^{10}) \) \( 2656 q - 8 q^{4} - 4 q^{6} - 4 q^{10} - 8 q^{16} - 8 q^{19} - 40 q^{21} - 20 q^{24} - 10 q^{30} - 36 q^{36} - 16 q^{39} + 24 q^{40} - 12 q^{45} + 24 q^{46} + 1216 q^{49} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 24 q^{60} - 8 q^{61} - 32 q^{64} + 64 q^{66} + 20 q^{69} - 168 q^{70} - 8 q^{75} - 8 q^{76} - 8 q^{81} - 128 q^{84} - 24 q^{85} + 60 q^{90} - 72 q^{91} + 8 q^{94} - 192 q^{96} + 184 q^{99} + O(q^{100}) \)

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.