Properties

Label 1175.4.e
Level $1175$
Weight $4$
Character orbit 1175.e
Rep. character $\chi_{1175}(93,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $428$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1175.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 235 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 732 436 296
Cusp forms 708 428 280
Eisenstein series 24 8 16

Trace form

\( 428 q + 4 q^{2} + 12 q^{3} + 72 q^{6} + 12 q^{7} - 112 q^{8} + O(q^{10}) \) \( 428 q + 4 q^{2} + 12 q^{3} + 72 q^{6} + 12 q^{7} - 112 q^{8} + 8 q^{12} - 6808 q^{16} + 132 q^{17} + 80 q^{18} - 584 q^{21} - 360 q^{27} - 1048 q^{28} - 892 q^{32} + 12760 q^{36} + 196 q^{37} - 952 q^{42} - 862 q^{47} - 208 q^{48} + 248 q^{51} + 492 q^{53} + 4344 q^{56} + 4200 q^{61} - 900 q^{63} - 848 q^{68} - 4520 q^{71} + 2268 q^{72} - 25076 q^{81} - 2308 q^{83} - 20744 q^{96} + 2308 q^{97} - 10008 q^{98} + O(q^{100}) \)

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(1175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1175, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(235, [\chi])\)\(^{\oplus 2}\)