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Properties

Label 3120.2.bz
Level $3120$
Weight $2$
Character orbit 3120.bz
Rep. character $\chi_{3120}(1379,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1152$
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.bz (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
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 1152 208
Cusp forms 1328 1152 176
Eisenstein series 32 0 32

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q - 8 q^{16} - 16 q^{19} - 12 q^{30} + 72 q^{34} + 80 q^{36} - 32 q^{40} + 56 q^{46} - 1152 q^{49} - 56 q^{54} + 32 q^{55} - 68 q^{60} - 32 q^{61} + 48 q^{64} + 120 q^{66} - 96 q^{70} + 56 q^{75} + 136 q^{76} - 56 q^{84} - 60 q^{90} - 88 q^{94} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \)