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Properties

Label 1320.2.dh
Level $1320$
Weight $2$
Character orbit 1320.dh
Rep. character $\chi_{1320}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2240$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1320.dh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1320 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

Total New Old
Modular forms 2368 2368 0
Cusp forms 2240 2240 0
Eisenstein series 128 128 0

Trace form

\( 2240 q - 12 q^{6} - 24 q^{7} + O(q^{10}) \) \( 2240 q - 12 q^{6} - 24 q^{7} - 16 q^{10} - 4 q^{12} - 12 q^{15} - 24 q^{16} + 2 q^{18} - 24 q^{25} - 44 q^{28} + 14 q^{30} - 48 q^{31} - 4 q^{33} + 4 q^{36} - 28 q^{40} - 6 q^{42} - 24 q^{46} - 18 q^{48} + 44 q^{52} + 8 q^{55} + 12 q^{57} - 52 q^{58} - 82 q^{60} - 68 q^{63} - 36 q^{66} - 52 q^{70} + 116 q^{72} - 24 q^{73} + 48 q^{76} - 20 q^{78} - 24 q^{81} - 52 q^{82} - 56 q^{87} - 208 q^{88} - 88 q^{90} - 128 q^{96} - 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.