Properties

Label 1380.2.bg
Level $1380$
Weight $2$
Character orbit 1380.bg
Rep. character $\chi_{1380}(221,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
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.bg (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
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 320 2680
Cusp forms 2760 320 2440
Eisenstein series 240 0 240

Trace form

\( 320q - 4q^{9} + O(q^{10}) \) \( 320q - 4q^{9} - 66q^{21} - 32q^{25} - 42q^{27} - 8q^{31} + 28q^{39} + 88q^{43} + 116q^{49} + 44q^{55} + 66q^{57} + 44q^{61} + 110q^{63} + 44q^{67} - 8q^{69} + 52q^{73} + 44q^{79} + 24q^{81} + 152q^{87} + 20q^{93} + 132q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)