↑

Properties

Label 1380.4.bj
Level $1380$
Weight $4$
Character orbit 1380.bj
Rep. character $\chi_{1380}(49,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $720$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1380.bj (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 8760 720 8040
Cusp forms 8520 720 7800
Eisenstein series 240 0 240

Trace form

\( 720 q + 16 q^{5} + 648 q^{9} + O(q^{10}) \) \( 720 q + 16 q^{5} + 648 q^{9} + 56 q^{11} - 24 q^{15} - 336 q^{19} + 168 q^{21} + 376 q^{25} - 48 q^{29} - 128 q^{31} + 32 q^{35} - 108 q^{39} - 328 q^{41} - 144 q^{45} + 3568 q^{49} + 744 q^{51} - 3252 q^{55} + 6028 q^{59} + 2760 q^{61} - 344 q^{65} - 576 q^{69} - 680 q^{71} - 1152 q^{75} - 3904 q^{79} - 5832 q^{81} + 1332 q^{85} - 2008 q^{89} - 14576 q^{91} + 13964 q^{95} + 5040 q^{99} + O(q^{100}) \)

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

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