Properties

Label 36.4.e
Level $36$
Weight $4$
Character orbit 36.e
Rep. character $\chi_{36}(13,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(36, [\chi])\).

Total New Old
Modular forms 42 6 36
Cusp forms 30 6 24
Eisenstein series 12 0 12

Trace form

\( 6q - 3q^{3} + 6q^{5} - 6q^{7} + 39q^{9} + O(q^{10}) \) \( 6q - 3q^{3} + 6q^{5} - 6q^{7} + 39q^{9} + 51q^{11} + 12q^{13} - 180q^{15} - 222q^{17} + 30q^{19} - 120q^{21} + 210q^{23} - 3q^{25} + 648q^{27} + 456q^{29} + 48q^{31} - 603q^{33} - 1104q^{35} - 96q^{37} - 36q^{39} + 897q^{41} + 129q^{43} + 1494q^{45} + 522q^{47} - 225q^{49} - 1647q^{51} - 2208q^{53} - 216q^{55} - 645q^{57} + 453q^{59} - 402q^{61} + 1896q^{63} + 1110q^{65} - 213q^{67} - 198q^{69} + 120q^{71} + 750q^{73} + 921q^{75} + 1128q^{77} + 552q^{79} - 549q^{81} - 612q^{83} + 1188q^{85} - 1386q^{87} - 924q^{89} - 264q^{91} - 1998q^{93} - 2184q^{95} + 93q^{97} - 1854q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
36.4.e.a \(6\) \(2.124\) 6.0.6831243.2 None \(0\) \(-3\) \(6\) \(-6\) \(q+(-1-\beta _{2})q^{3}+(1-3\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)