Space of modular forms of level 230, weight 4, and Character 230.e

• Label: 230.4.e
• Level: $230$
• Weight: $4$
• Character orbit: 230.e
• Rep. character: $\chi_{230}(137,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(230, [\chi])\).

	Total	New	Old
Modular forms	224	72	152
Cusp forms	208	72	136
Eisenstein series	16	0	16

Trace form

72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(230, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
230.4.e.a	$230$	$4$	230.e	115.e	$4$	$72$	$36$	$13.570$		None		✓	✓	✓	230.4.e.a	$4$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(230, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)