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Properties

Label 1380.4.r
Level $1380$
Weight $4$
Character orbit 1380.r
Rep. character $\chi_{1380}(737,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $264$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
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 264 1488
Cusp forms 1704 264 1440
Eisenstein series 48 0 48

Trace form

\( 264 q - 24 q^{7} + O(q^{10}) \) \( 264 q - 24 q^{7} + 48 q^{13} - 168 q^{15} + 224 q^{21} + 288 q^{27} - 288 q^{31} + 1048 q^{33} - 528 q^{37} - 2720 q^{45} - 3408 q^{51} + 1992 q^{55} + 1728 q^{57} + 1728 q^{61} + 2288 q^{63} - 288 q^{67} - 4824 q^{73} - 5008 q^{75} - 1664 q^{81} + 6768 q^{85} + 4672 q^{87} + 4320 q^{91} + 6856 q^{93} + 216 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)