Space of modular forms of level 204, weight 4, and Character 204.l

• Label: 204.4.l
• Level: $204$
• Weight: $4$
• Character orbit: 204.l
• Rep. character: $\chi_{204}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $208$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 204 = 2^{2} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	204.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 204 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(204, [\chi])\).

	Total	New	Old
Modular forms	224	224	0
Cusp forms	208	208	0
Eisenstein series	16	16	0

Trace form

208 * q - 8 * q^4 + 14 * q^6 - 96 * q^10 - 58 * q^12 - 16 * q^13 + 256 * q^16 - 36 * q^18 - 8 * q^21 + 280 * q^22 + 302 * q^24 + 720 * q^28 + 608 * q^30 + 528 * q^33 + 888 * q^34 + 520 * q^37 - 1068 * q^40 - 504 * q^45 - 1100 * q^46 + 1274 * q^48 - 2176 * q^52 + 410 * q^54 - 1528 * q^57 + 828 * q^58 - 1208 * q^61 + 1504 * q^64 + 1032 * q^69 - 2556 * q^72 - 1664 * q^73 - 1484 * q^78 - 4608 * q^81 + 1908 * q^82 + 5800 * q^84 + 1288 * q^85 + 1828 * q^88 - 2816 * q^90 - 6526 * q^96 + 64 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(204, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
204.4.l.a	$204$	$4$	204.l	204.l	$4$	$208$	$104$	$12.036$		None		✓	✓	✓	204.4.l.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$