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Properties

Label 1320.2.cy
Level $1320$
Weight $2$
Character orbit 1320.cy
Rep. character $\chi_{1320}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
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.cy (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 144 1072
Cusp forms 1088 144 944
Eisenstein series 128 0 128

Trace form

\( 144 q + 36 q^{9} + O(q^{10}) \) \( 144 q + 36 q^{9} - 4 q^{11} + 6 q^{15} + 32 q^{19} - 32 q^{21} - 20 q^{31} + 36 q^{35} + 8 q^{39} - 36 q^{41} + 96 q^{49} - 24 q^{51} + 52 q^{55} + 8 q^{59} + 24 q^{61} - 24 q^{65} + 32 q^{71} - 8 q^{75} - 20 q^{79} - 36 q^{81} + 52 q^{85} - 8 q^{89} + 20 q^{91} + 56 q^{95} + 4 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)