Properties

Label 360.2.bm
Level $360$
Weight $2$
Character orbit 360.bm
Rep. character $\chi_{360}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 152 96 56
Cusp forms 136 96 40
Eisenstein series 16 0 16

Trace form

\( 96q + 6q^{6} + O(q^{10}) \) \( 96q + 6q^{6} - 2q^{12} + 30q^{14} - 4q^{18} - 28q^{24} - 48q^{25} + 24q^{27} - 16q^{30} - 16q^{33} + 6q^{34} - 54q^{36} - 60q^{38} + 6q^{40} + 24q^{41} - 62q^{42} - 12q^{46} + 52q^{48} + 48q^{49} - 40q^{51} + 18q^{52} - 68q^{54} + 42q^{56} + 8q^{57} - 18q^{58} - 72q^{59} + 14q^{60} - 24q^{64} - 8q^{66} + 108q^{68} + 52q^{72} + 84q^{74} + 6q^{76} + 54q^{78} - 16q^{81} - 36q^{82} - 120q^{83} + 10q^{84} + 54q^{86} - 18q^{90} - 60q^{92} - 18q^{94} - 106q^{96} - 32q^{99} + O(q^{100}) \)

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.bm.a \(48\) \(2.875\) None \(0\) \(0\) \(-24\) \(0\)
360.2.bm.b \(48\) \(2.875\) None \(0\) \(0\) \(24\) \(0\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)