Properties

Label 2880.2.z
Level $2880$
Weight $2$
Character orbit 2880.z
Rep. character $\chi_{2880}(847,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $116$
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.z (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1216 124 1092
Cusp forms 1088 116 972
Eisenstein series 128 8 120

Trace form

\( 116q + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 116q + 2q^{5} + 4q^{7} - 4q^{11} + 4q^{17} - 8q^{19} - 4q^{23} - 4q^{35} - 24q^{47} + 4q^{53} + 4q^{55} - 16q^{59} - 20q^{61} + 4q^{65} - 40q^{71} - 8q^{73} + 32q^{77} - 44q^{83} + 8q^{85} - 12q^{91} - 40q^{95} - 4q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)