Properties

Label 1380.2.bj
Level $1380$
Weight $2$
Character orbit 1380.bj
Rep. character $\chi_{1380}(49,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $240$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.bj (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 3000 240 2760
Cusp forms 2760 240 2520
Eisenstein series 240 0 240

Trace form

\( 240q - 4q^{5} + 24q^{9} + O(q^{10}) \) \( 240q - 4q^{5} + 24q^{9} + 16q^{11} + 4q^{15} - 8q^{19} - 8q^{21} - 28q^{25} - 12q^{29} + 4q^{31} - 20q^{35} + 36q^{39} + 4q^{41} + 4q^{45} + 20q^{49} - 16q^{51} - 6q^{55} + 80q^{59} + 12q^{61} + 32q^{65} - 28q^{71} + 24q^{75} - 68q^{79} - 24q^{81} - 62q^{85} + 16q^{89} + 144q^{91} - 50q^{95} + 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)