Properties

Label 90.2.l
Level $90$
Weight $2$
Character orbit 90.l
Rep. character $\chi_{90}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $24$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 90.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(90, [\chi])\).

Total New Old
Modular forms 88 24 64
Cusp forms 56 24 32
Eisenstein series 32 0 32

Trace form

\( 24q + 4q^{3} - 8q^{6} + O(q^{10}) \) \( 24q + 4q^{3} - 8q^{6} - 24q^{11} - 4q^{12} - 8q^{15} + 12q^{16} - 8q^{18} - 12q^{20} - 8q^{21} - 24q^{23} - 12q^{25} - 8q^{27} - 24q^{30} + 16q^{33} + 16q^{36} - 24q^{37} + 36q^{38} + 36q^{41} + 44q^{42} + 68q^{45} - 24q^{46} + 48q^{47} + 8q^{48} + 48q^{50} - 16q^{51} - 24q^{55} + 12q^{56} + 52q^{57} + 12q^{58} + 4q^{60} - 12q^{61} - 80q^{63} - 24q^{65} - 8q^{66} - 12q^{67} - 36q^{68} - 16q^{72} + 8q^{75} - 48q^{77} - 24q^{78} - 4q^{81} - 48q^{82} + 60q^{83} - 24q^{85} - 72q^{86} - 56q^{87} - 8q^{90} + 48q^{91} - 24q^{92} + 52q^{93} + 60q^{95} - 4q^{96} - 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(90, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
90.2.l.a \(8\) \(0.719\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(12\) \(-8\) \(q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
90.2.l.b \(16\) \(0.719\) 16.0.\(\cdots\).9 None \(0\) \(0\) \(-12\) \(8\) \(q-\beta _{11}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

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