Properties

Label 360.2.bo
Level $360$
Weight $2$
Character orbit 360.bo
Rep. character $\chi_{360}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $272$
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.bo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
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 304 304 0
Cusp forms 272 272 0
Eisenstein series 32 32 0

Trace form

\( 272q - 2q^{2} - 8q^{3} - 8q^{6} - 8q^{8} + O(q^{10}) \) \( 272q - 2q^{2} - 8q^{3} - 8q^{6} - 8q^{8} - 8q^{10} - 8q^{11} - 10q^{12} - 4q^{16} - 16q^{17} + 20q^{18} + 14q^{20} + 6q^{22} - 4q^{25} - 48q^{26} - 8q^{27} + 8q^{28} - 34q^{30} - 22q^{32} + 4q^{33} - 16q^{35} - 8q^{36} - 26q^{38} - 2q^{40} - 8q^{41} - 66q^{42} - 4q^{43} - 40q^{46} - 38q^{48} - 42q^{50} - 16q^{51} + 14q^{52} + 24q^{56} + 16q^{57} + 6q^{58} + 14q^{60} - 76q^{62} - 4q^{65} - 44q^{66} - 4q^{67} - 46q^{68} + 18q^{70} + 38q^{72} - 16q^{73} - 120q^{75} - 38q^{78} + 92q^{80} - 32q^{81} - 4q^{83} - 40q^{86} - 42q^{88} - 14q^{90} - 32q^{91} + 52q^{92} + 108q^{96} - 4q^{97} - 140q^{98} + O(q^{100}) \)

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.bo.a \(272\) \(2.875\) None \(-2\) \(-8\) \(0\) \(0\)