Properties

Label 360.2.bf
Level $360$
Weight $2$
Character orbit 360.bf
Rep. character $\chi_{360}(61,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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.bf (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: \(1\)
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 96 56
Cusp forms 136 96 40
Eisenstein series 16 0 16

Trace form

\( 96q - 6q^{6} + 12q^{8} + O(q^{10}) \) \( 96q - 6q^{6} + 12q^{8} + 22q^{12} - 10q^{14} - 4q^{18} + 24q^{23} + 12q^{24} + 48q^{25} - 40q^{26} - 16q^{30} - 20q^{32} + 16q^{33} + 6q^{34} - 38q^{36} - 20q^{38} - 24q^{39} + 6q^{40} - 8q^{41} + 22q^{42} - 76q^{44} + 12q^{46} - 40q^{47} - 76q^{48} - 48q^{49} - 18q^{52} + 24q^{54} - 54q^{56} + 8q^{57} + 18q^{58} - 14q^{60} + 76q^{62} - 80q^{63} - 48q^{64} + 36q^{66} + 16q^{68} + 104q^{72} + 56q^{74} - 6q^{76} + 94q^{78} - 16q^{80} - 36q^{82} + 86q^{84} - 70q^{86} - 48q^{87} - 16q^{89} - 18q^{90} + 36q^{92} - 18q^{94} - 32q^{95} - 38q^{96} - 24q^{98} + O(q^{100}) \)

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.bf.a \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(8\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
360.2.bf.b \(92\) \(2.875\) None \(2\) \(0\) \(0\) \(-8\)

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

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