Space of modular forms of level 204, weight 2, and Character 204.b

• Label: 204.2.b
• Level: $204$
• Weight: $2$
• Character orbit: 204.b
• Rep. character: $\chi_{204}(169,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 204 = 2^{2} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	204.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(204, [\chi])\).

	Total	New	Old
Modular forms	42	2	40
Cusp forms	30	2	28
Eisenstein series	12	0	12

Trace form

\( 2 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(204, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
204.2.b.a	$204$	$2$	204.b	17.b	$2$	$2$	$2$	$1.629$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+2iq^{7}-q^{9}+3iq^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(204, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(204, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)