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Properties

Label 1320.2.cw
Level $1320$
Weight $2$
Character orbit 1320.cw
Rep. character $\chi_{1320}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
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.cw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1216 192 1024
Cusp forms 1088 192 896
Eisenstein series 128 0 128

Trace form

\( 192 q + 4 q^{3} + 12 q^{9} + O(q^{10}) \) \( 192 q + 4 q^{3} + 12 q^{9} - 60 q^{19} + 48 q^{25} + 4 q^{27} + 8 q^{31} + 22 q^{33} - 8 q^{37} + 60 q^{39} + 40 q^{49} + 70 q^{51} + 16 q^{55} + 30 q^{57} + 40 q^{61} + 80 q^{63} - 24 q^{67} - 24 q^{69} + 40 q^{73} + 6 q^{75} + 20 q^{79} + 68 q^{81} - 32 q^{91} - 32 q^{93} + 100 q^{97} + 32 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)