Properties

Label 2280.2.dc
Level $2280$
Weight $2$
Character orbit 2280.dc
Rep. character $\chi_{2280}(481,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $240$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2280.dc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2280, [\chi])\).

Total New Old
Modular forms 2976 240 2736
Cusp forms 2784 240 2544
Eisenstein series 192 0 192

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 12 q^{13} + 24 q^{17} - 12 q^{19} - 12 q^{21} - 12 q^{27} - 48 q^{29} - 24 q^{31} + 12 q^{35} - 84 q^{41} - 12 q^{43} - 48 q^{47} - 144 q^{49} - 72 q^{53} - 48 q^{61} + 24 q^{63} + 36 q^{65} - 12 q^{67} + 168 q^{71} + 12 q^{73} + 24 q^{75} + 72 q^{79} + 72 q^{83} + 48 q^{91} + 24 q^{93} - 120 q^{97} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)