↑

Properties

Label 1175.4.l
Level $1175$
Weight $4$
Character orbit 1175.l
Rep. character $\chi_{1175}(187,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2864$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1175.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1175, [\chi])\).

Total New Old
Modular forms 2896 2896 0
Cusp forms 2864 2864 0
Eisenstein series 32 32 0

Trace form

\( 2864 q - 16 q^{2} - 8 q^{3} - 20 q^{4} - 12 q^{6} - 8 q^{7} - 132 q^{8} - 20 q^{9} + O(q^{10}) \) \( 2864 q - 16 q^{2} - 8 q^{3} - 20 q^{4} - 12 q^{6} - 8 q^{7} - 132 q^{8} - 20 q^{9} - 12 q^{12} - 20 q^{14} + 11252 q^{16} - 528 q^{17} + 60 q^{18} - 12 q^{21} - 944 q^{25} + 700 q^{27} - 1068 q^{28} - 912 q^{32} - 20 q^{34} - 25580 q^{36} + 176 q^{37} - 972 q^{42} - 2592 q^{47} - 68 q^{48} + 8032 q^{50} - 32 q^{51} + 472 q^{53} - 20 q^{54} + 460 q^{55} - 524 q^{56} + 3300 q^{59} - 12 q^{61} - 920 q^{63} + 3880 q^{64} + 1936 q^{65} - 868 q^{68} - 2492 q^{71} + 2788 q^{72} + 5552 q^{75} - 20 q^{79} + 54112 q^{81} + 11512 q^{83} - 20 q^{84} - 20 q^{89} + 11030 q^{94} - 10804 q^{95} + 5964 q^{96} + 2288 q^{97} + 17292 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1175, [\chi])\) into newform subspaces

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