Properties

Label 36.2.e
Level $36$
Weight $2$
Character orbit 36.e
Rep. character $\chi_{36}(13,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 36.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

Trace form

\( 2 q - 3 q^{5} + q^{7} - 6 q^{9} + O(q^{10}) \) \( 2 q - 3 q^{5} + q^{7} - 6 q^{9} - 3 q^{11} + q^{13} + 9 q^{15} + 12 q^{17} - 8 q^{19} + 3 q^{21} + 3 q^{23} - 4 q^{25} - 3 q^{29} - 5 q^{31} - 9 q^{33} - 6 q^{35} + 4 q^{37} - 3 q^{39} - 3 q^{41} + q^{43} + 9 q^{45} + 9 q^{47} + 6 q^{49} - 12 q^{53} + 18 q^{55} + 3 q^{59} + 13 q^{61} - 3 q^{63} + 3 q^{65} + 7 q^{67} - 9 q^{69} - 24 q^{71} - 20 q^{73} - 12 q^{75} + 3 q^{77} - 11 q^{79} + 18 q^{81} + 9 q^{83} - 18 q^{85} - 9 q^{87} + 12 q^{89} + 2 q^{91} + 15 q^{93} + 12 q^{95} - 11 q^{97} + 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.2.e.a 36.e 9.c $2$ $0.287$ \(\Q(\sqrt{-3}) \) None 36.2.e.a \(0\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)