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Properties

Label 3120.2.hl
Level $3120$
Weight $2$
Character orbit 3120.hl
Rep. character $\chi_{3120}(1069,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1344$
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.hl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1040 \)
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 1344 1376
Cusp forms 2656 1344 1312
Eisenstein series 64 0 64

Trace form

\( 1344 q + O(q^{10}) \) \( 1344 q + 32 q^{14} - 80 q^{26} + 8 q^{30} - 32 q^{44} - 672 q^{49} - 20 q^{50} - 32 q^{59} + 48 q^{60} - 16 q^{65} - 168 q^{70} + 16 q^{75} - 64 q^{76} - 320 q^{79} + 672 q^{81} - 128 q^{86} + 16 q^{90} - 64 q^{91} + 32 q^{94} + 80 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 2}\)