Properties

Label 1380.2.s
Level $1380$
Weight $2$
Character orbit 1380.s
Rep. character $\chi_{1380}(967,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $264$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 264 328
Cusp forms 560 264 296
Eisenstein series 32 0 32

Trace form

\( 264q + 24q^{8} + O(q^{10}) \) \( 264q + 24q^{8} + 16q^{10} + 16q^{12} + 8q^{13} - 32q^{16} + 40q^{17} + 16q^{22} + 40q^{25} - 32q^{26} - 24q^{28} - 16q^{30} - 16q^{33} - 8q^{37} - 32q^{38} + 16q^{40} - 8q^{45} - 16q^{52} - 8q^{53} + 32q^{56} + 8q^{58} - 40q^{65} + 48q^{66} + 32q^{68} + 24q^{70} + 24q^{72} - 88q^{73} + 48q^{76} + 48q^{78} - 264q^{81} + 8q^{82} + 8q^{85} + 32q^{86} - 120q^{88} - 24q^{90} + 40q^{97} + 8q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)