Properties

Label 360.2.bk
Level $360$
Weight $2$
Character orbit 360.bk
Rep. character $\chi_{360}(229,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $136$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
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 152 152 0
Cusp forms 136 136 0
Eisenstein series 16 16 0

Trace form

\( 136q - 2q^{4} - 8q^{9} + O(q^{10}) \) \( 136q - 2q^{4} - 8q^{9} - 10q^{14} + 2q^{15} - 2q^{16} - 2q^{20} - 38q^{24} - 2q^{25} + 16q^{26} - 12q^{30} - 4q^{31} + 8q^{34} - 24q^{36} + 4q^{39} - 6q^{40} - 4q^{41} - 56q^{44} - 28q^{46} + 40q^{49} - 12q^{50} + 10q^{54} - 28q^{55} + 26q^{56} - 58q^{60} - 20q^{64} + 18q^{65} + 16q^{66} - 6q^{70} - 128q^{71} + 36q^{74} + 12q^{76} - 4q^{79} - 36q^{80} - 16q^{81} - 110q^{84} + 44q^{86} - 32q^{89} + 32q^{90} - 34q^{94} + 8q^{95} - 2q^{96} + O(q^{100}) \)

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.bk.a \(136\) \(2.875\) None \(0\) \(0\) \(0\) \(0\)