Space of modular forms of level 9036, weight 2, and Character 9036.e

• Label: 9036.2.e
• Level: $9036$
• Weight: $2$
• Character orbit: 9036.e
• Rep. character: $\chi_{9036}(4517,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $1$
• Sturm bound: $3024$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9036.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 753 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3024\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(9036, [\chi])\).

	Total	New	Old
Modular forms	1524	84	1440
Cusp forms	1500	84	1416
Eisenstein series	24	0	24

Trace form

\( 84 q - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(9036, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9036.2.e.a	$9036$	$2$	9036.e	753.d	$2$	$84$	$84$	$72.153$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(9036, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(9036, [\chi]) \cong \)