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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

\( 10q + 12q^{3} - 21q^{5} + 29q^{7} + 12q^{9} + O(q^{10}) \) \( 10q + 12q^{3} - 21q^{5} + 29q^{7} + 12q^{9} + 177q^{11} - 181q^{13} + 117q^{15} + 2280q^{17} - 832q^{19} - 207q^{21} + 399q^{23} - 4778q^{25} - 7128q^{27} - 6033q^{29} + 2759q^{31} + 9603q^{33} + 37146q^{35} - 15172q^{37} + 5529q^{39} - 18435q^{41} + 1469q^{43} - 64089q^{45} - 25155q^{47} - 4056q^{49} + 90612q^{51} + 116844q^{53} + 14778q^{55} + 26934q^{57} - 90537q^{59} + 1403q^{61} - 198255q^{63} - 148407q^{65} + 13907q^{67} + 214425q^{69} + 229368q^{71} + 15200q^{73} + 44640q^{75} - 211983q^{77} + 29993q^{79} - 404172q^{81} - 228951q^{83} - 49662q^{85} + 397323q^{87} + 598332q^{89} + 124930q^{91} + 250041q^{93} - 394764q^{95} + 40541q^{97} - 697239q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
36.6.e.a \(10\) \(5.774\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(12\) \(-21\) \(29\) \(q+(2+2\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(4\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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