Properties

Label 360.2.bs
Level $360$
Weight $2$
Character orbit 360.bs
Rep. character $\chi_{360}(113,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 320 72 248
Cusp forms 256 72 184
Eisenstein series 64 0 64

Trace form

\( 72q + O(q^{10}) \) \( 72q + 12q^{15} + 16q^{21} + 24q^{23} - 12q^{27} + 12q^{33} + 12q^{41} - 16q^{45} - 36q^{47} + 24q^{51} - 40q^{57} + 12q^{61} - 44q^{63} - 72q^{65} - 36q^{75} - 48q^{77} - 20q^{81} - 60q^{83} + 24q^{85} - 40q^{87} - 84q^{93} - 60q^{95} + 24q^{97} + O(q^{100}) \)

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.bs.a \(72\) \(2.875\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)