Properties

Label 555.2.g
Level $555$
Weight $2$
Character orbit 555.g
Rep. character $\chi_{555}(184,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $152$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(555, [\chi])\).

Total New Old
Modular forms 80 40 40
Cusp forms 72 40 32
Eisenstein series 8 0 8

Trace form

\( 40q + 44q^{4} - 40q^{9} + O(q^{10}) \) \( 40q + 44q^{4} - 40q^{9} + 4q^{10} + 8q^{11} + 52q^{16} - 16q^{21} + 8q^{25} - 16q^{26} + 16q^{30} - 32q^{34} - 44q^{36} - 28q^{40} + 8q^{41} + 16q^{44} - 8q^{46} - 24q^{49} + 92q^{64} - 48q^{65} - 56q^{70} + 24q^{71} - 68q^{74} + 8q^{75} + 40q^{81} - 16q^{84} - 64q^{85} + 80q^{86} - 4q^{90} + 32q^{95} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(555, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
555.2.g.a \(40\) \(4.432\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(555, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(555, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)