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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

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

Display 100 coefficients 10 coefficients

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

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