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Properties

Label 3120.2.ev
Level $3120$
Weight $2$
Character orbit 3120.ev
Rep. character $\chi_{3120}(131,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $768$
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.ev (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 768 592
Cusp forms 1328 768 560
Eisenstein series 32 0 32

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 8 q^{10} + 72 q^{16} + 40 q^{18} - 16 q^{19} + 40 q^{24} + 8 q^{34} - 56 q^{46} - 40 q^{48} + 768 q^{49} + 80 q^{51} - 144 q^{54} + 64 q^{58} - 56 q^{60} + 32 q^{61} + 48 q^{64} - 40 q^{66} + 128 q^{67} + 56 q^{76} + 32 q^{84} + 32 q^{85} + 64 q^{88} - 104 q^{94} - 136 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)