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Properties

Label 3120.2.bm
Level $3120$
Weight $2$
Character orbit 3120.bm
Rep. character $\chi_{3120}(1091,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $896$
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.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
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 896 464
Cusp forms 1328 896 432
Eisenstein series 32 0 32

Trace form

\( 896 q + O(q^{10}) \) \( 896 q - 24 q^{12} + 48 q^{22} + 48 q^{27} + 24 q^{36} + 48 q^{39} + 40 q^{42} + 40 q^{48} - 896 q^{49} - 8 q^{52} - 144 q^{64} + 72 q^{66} + 64 q^{78} + 224 q^{82} - 80 q^{88} - 72 q^{90} + 48 q^{91} - 48 q^{94} + O(q^{100}) \)

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

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