Properties

Label 360.2.bd
Level $360$
Weight $2$
Character orbit 360.bd
Rep. character $\chi_{360}(59,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $136$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

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

Trace form

\( 136q - 2q^{4} - 8q^{9} + O(q^{10}) \) \( 136q - 2q^{4} - 8q^{9} - 8q^{10} - 12q^{11} - 6q^{14} - 2q^{16} - 16q^{19} - 24q^{20} - 10q^{24} - 2q^{25} - 10q^{30} + 32q^{36} + 4q^{40} - 12q^{41} - 4q^{46} - 48q^{49} - 42q^{50} - 32q^{51} - 62q^{54} - 6q^{56} - 12q^{59} - 24q^{60} + 4q^{64} - 6q^{65} + 44q^{66} - 60q^{74} + 46q^{75} - 16q^{76} + 94q^{84} - 62q^{90} + 40q^{91} + 14q^{94} - 22q^{96} - 76q^{99} + O(q^{100}) \)

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.bd.a \(8\) \(2.875\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
360.2.bd.b \(128\) \(2.875\) None \(0\) \(0\) \(0\) \(0\)