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Properties

Label 1320.2.dm
Level $1320$
Weight $2$
Character orbit 1320.dm
Rep. character $\chi_{1320}(163,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1152$
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.dm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
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 1152 1216
Cusp forms 2240 1152 1088
Eisenstein series 128 0 128

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q - 16 q^{10} + 16 q^{12} + 16 q^{16} - 60 q^{20} + 28 q^{22} + 16 q^{26} + 24 q^{30} - 40 q^{32} - 56 q^{38} + 24 q^{40} + 64 q^{43} + 144 q^{46} - 40 q^{50} + 24 q^{52} + 160 q^{56} - 32 q^{58} - 40 q^{62} + 24 q^{66} - 144 q^{68} - 48 q^{76} - 96 q^{78} - 40 q^{80} + 288 q^{81} - 64 q^{82} + 240 q^{83} + 112 q^{86} - 76 q^{88} - 64 q^{91} + 100 q^{92} + 32 q^{97} - 240 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)