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Properties

Label 1380.4.t
Level $1380$
Weight $4$
Character orbit 1380.t
Rep. character $\chi_{1380}(1057,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1380.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1380, [\chi])\).

Total New Old
Modular forms 1752 144 1608
Cusp forms 1704 144 1560
Eisenstein series 48 0 48

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 96 q^{13} + 232 q^{23} + 592 q^{25} - 256 q^{31} + 688 q^{35} + 528 q^{41} - 1664 q^{47} + 928 q^{55} - 432 q^{71} + 144 q^{73} - 1248 q^{75} + 2240 q^{77} - 11664 q^{81} - 5536 q^{85} + 960 q^{87} - 720 q^{93} + 240 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

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