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Properties

Label 36.5.g
Level $36$
Weight $5$
Character orbit 36.g
Rep. character $\chi_{36}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 36.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(36, [\chi])\).

Total New Old
Modular forms 54 8 46
Cusp forms 42 8 34
Eisenstein series 12 0 12

Trace form

\( 8 q - 9 q^{3} - 9 q^{5} + 13 q^{7} + 21 q^{9} + O(q^{10}) \) \( 8 q - 9 q^{3} - 9 q^{5} + 13 q^{7} + 21 q^{9} - 18 q^{11} - 5 q^{13} + 225 q^{15} + 562 q^{19} - 1167 q^{21} - 1719 q^{23} + 353 q^{25} + 648 q^{27} + 2115 q^{29} + 187 q^{31} + 3258 q^{33} + 16 q^{37} - 8265 q^{39} - 7920 q^{41} - 68 q^{43} + 5679 q^{45} + 13689 q^{47} - 327 q^{49} + 10449 q^{51} - 1818 q^{55} - 21861 q^{57} - 20052 q^{59} - 1937 q^{61} + 5559 q^{63} + 25965 q^{65} + 154 q^{67} + 21645 q^{69} - 7802 q^{73} - 30297 q^{75} - 25641 q^{77} - 2195 q^{79} + 19701 q^{81} + 37017 q^{83} - 3042 q^{85} + 22455 q^{87} + 15830 q^{91} - 36489 q^{93} - 37116 q^{95} + 7282 q^{97} - 10035 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.5.g.a 36.g 9.d $8$ $3.721$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-9\) \(-9\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)