Properties

Label 2880.2.dk
Level $2880$
Weight $2$
Character orbit 2880.dk
Rep. character $\chi_{2880}(257,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.dk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

Total New Old
Modular forms 2400 592 1808
Cusp forms 2208 560 1648
Eisenstein series 192 32 160

Trace form

\( 560q + 12q^{5} + O(q^{10}) \) \( 560q + 12q^{5} + 4q^{13} + 16q^{21} - 4q^{25} - 20q^{33} + 16q^{37} - 24q^{41} - 12q^{45} + 16q^{57} + 8q^{61} - 12q^{65} - 16q^{73} + 12q^{77} + 16q^{81} + 4q^{85} + 92q^{93} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)