Properties

Label 36.6.e
Level $36$
Weight $6$
Character orbit 36.e
Rep. character $\chi_{36}(13,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
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: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(36, [\chi])\).

Total New Old
Modular forms 66 10 56
Cusp forms 54 10 44
Eisenstein series 12 0 12

Trace form

\( 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9} + 177 q^{11} - 181 q^{13} + 117 q^{15} + 2280 q^{17} - 832 q^{19} - 207 q^{21} + 399 q^{23} - 4778 q^{25} - 7128 q^{27} - 6033 q^{29} + 2759 q^{31} + 9603 q^{33}+ \cdots - 697239 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.6.e.a 36.e 9.c $10$ $5.774$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 36.6.e.a \(0\) \(12\) \(-21\) \(29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(4\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)