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Properties

Label 1480.2.ce
Level $1480$
Weight $2$
Character orbit 1480.ce
Rep. character $\chi_{1480}(81,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $228$
Sturm bound $456$

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Defining parameters

Level: \( N \) \(=\) \( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1480.ce (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1480, [\chi])\).

Total New Old
Modular forms 1416 228 1188
Cusp forms 1320 228 1092
Eisenstein series 96 0 96

Trace form

\( 228 q + 12 q^{7} + O(q^{10}) \) \( 228 q + 12 q^{7} - 24 q^{13} - 6 q^{19} + 12 q^{21} + 48 q^{27} - 24 q^{31} + 12 q^{37} + 36 q^{39} + 60 q^{49} - 12 q^{55} - 36 q^{57} + 12 q^{59} + 84 q^{63} + 18 q^{65} + 36 q^{67} + 24 q^{69} + 12 q^{71} + 72 q^{73} - 24 q^{75} + 48 q^{77} + 12 q^{79} + 24 q^{83} - 12 q^{85} + 72 q^{87} + 6 q^{89} - 6 q^{91} + 12 q^{93} + 24 q^{97} + 78 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1480, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(740, [\chi])\)\(^{\oplus 2}\)