Properties

Label 135.2.e
Level $135$
Weight $2$
Character orbit 135.e
Rep. character $\chi_{135}(46,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(135, [\chi])\).

Total New Old
Modular forms 48 8 40
Cusp forms 24 8 16
Eisenstein series 24 0 24

Trace form

\( 8q + 2q^{2} - 4q^{4} + 2q^{5} - 2q^{7} + O(q^{10}) \) \( 8q + 2q^{2} - 4q^{4} + 2q^{5} - 2q^{7} - 4q^{11} - 2q^{13} - 12q^{14} - 4q^{16} - 4q^{17} - 8q^{19} + 6q^{20} + 6q^{22} + 6q^{23} - 4q^{25} + 8q^{26} + 16q^{28} - 8q^{29} - 8q^{31} + 22q^{32} - 16q^{35} + 4q^{37} - 10q^{38} - 6q^{40} - 8q^{41} - 2q^{43} + 40q^{44} + 20q^{47} + 2q^{50} + 10q^{52} + 8q^{53} + 18q^{58} - 16q^{59} - 8q^{61} - 84q^{62} - 16q^{64} + 6q^{65} - 8q^{67} - 26q^{68} + 6q^{70} + 16q^{71} - 8q^{73} - 20q^{74} + 4q^{76} + 6q^{77} + 4q^{79} - 12q^{80} - 48q^{82} - 6q^{83} + 6q^{85} + 20q^{86} + 18q^{88} + 48q^{89} + 32q^{91} + 36q^{92} + 24q^{94} + 12q^{95} + 16q^{97} + 76q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
135.2.e.a \(2\) \(1.078\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(3\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
135.2.e.b \(6\) \(1.078\) 6.0.954288.1 None \(1\) \(0\) \(3\) \(-5\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(135, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)