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

• Label: 204.2.p
• Level: $204$
• Weight: $2$
• Character orbit: 204.p
• Rep. character: $\chi_{204}(59,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $128$
• 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.p (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 204 \)
Character field:			\(\Q(\zeta_{8})\)
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	160	160	0
Cusp forms	128	128	0
Eisenstein series	32	32	0

Trace form

128 * q - 4 * q^6 - 16 * q^9 - 8 * q^10 - 16 * q^12 - 16 * q^16 - 8 * q^18 + 16 * q^22 - 24 * q^24 - 16 * q^25 - 64 * q^28 - 16 * q^33 - 64 * q^34 + 12 * q^36 - 16 * q^37 - 40 * q^40 - 32 * q^42 - 8 * q^45 - 72 * q^46 + 60 * q^48 - 16 * q^49 + 48 * q^52 + 16 * q^54 - 40 * q^57 - 40 * q^58 + 32 * q^60 - 80 * q^61 + 116 * q^66 - 48 * q^69 + 8 * q^70 - 16 * q^73 - 72 * q^76 + 72 * q^78 + 40 * q^82 + 64 * q^84 - 16 * q^85 + 24 * q^88 - 8 * q^93 + 48 * q^94 + 124 * q^96 - 64 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
204.2.p.a	$204$	$2$	204.p	204.p	$8$	$128$	$32$	$1.629$		None		✓	✓	✓	204.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$