Properties

Label 360.2.bi
Level $360$
Weight $2$
Character orbit 360.bi
Rep. character $\chi_{360}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 160 36 124
Cusp forms 128 36 92
Eisenstein series 32 0 32

Trace form

\( 36q - 2q^{9} + O(q^{10}) \) \( 36q - 2q^{9} + 12q^{11} + 2q^{15} - 4q^{21} + 6q^{29} + 12q^{35} - 16q^{39} - 18q^{41} + 26q^{45} + 24q^{49} - 48q^{51} + 12q^{55} - 24q^{59} - 6q^{61} + 18q^{65} - 10q^{69} - 24q^{71} - 10q^{75} + 12q^{79} - 70q^{81} + 12q^{85} - 36q^{89} - 36q^{95} - 40q^{99} + O(q^{100}) \)

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.bi.a \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
360.2.bi.b \(32\) \(2.875\) None \(0\) \(0\) \(-2\) \(0\)

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

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