Properties

Label 360.2.x
Level $360$
Weight $2$
Character orbit 360.x
Rep. character $\chi_{360}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(360, [\chi])\).

Total New Old
Modular forms 160 48 112
Cusp forms 128 48 80
Eisenstein series 32 0 32

Trace form

\( 48q + O(q^{10}) \) \( 48q + 16q^{10} - 8q^{16} + 16q^{22} - 32q^{28} + 32q^{31} - 56q^{40} - 16q^{46} - 56q^{52} - 80q^{58} - 64q^{70} + 48q^{76} - 48q^{82} + 64q^{88} - 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
360.2.x.a \(48\) \(2.875\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)