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

• Label: 230.4.g
• Level: $230$
• Weight: $4$
• Character orbit: 230.g
• Rep. character: $\chi_{230}(31,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $240$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1120	240	880
Cusp forms	1040	240	800
Eisenstein series	80	0	80

Trace form

240 * q - 96 * q^4 - 10 * q^5 - 8 * q^6 - 188 * q^9 - 20 * q^10 - 108 * q^11 - 32 * q^13 + 96 * q^14 - 384 * q^16 - 552 * q^17 - 224 * q^18 + 428 * q^19 - 40 * q^20 + 2184 * q^21 + 880 * q^22 - 132 * q^23 - 32 * q^24 - 600 * q^25 + 672 * q^26 - 408 * q^27 - 1284 * q^29 + 160 * q^30 - 2064 * q^31 + 424 * q^33 - 624 * q^34 - 1210 * q^35 - 752 * q^36 - 132 * q^37 - 520 * q^38 - 1100 * q^39 - 80 * q^40 + 2284 * q^41 - 128 * q^42 + 2636 * q^43 - 432 * q^44 + 2600 * q^45 - 264 * q^46 + 1320 * q^47 + 154 * q^49 + 456 * q^51 - 128 * q^52 - 56 * q^53 - 3732 * q^54 - 2100 * q^55 - 1552 * q^56 - 11616 * q^57 - 3104 * q^58 - 5346 * q^59 - 236 * q^61 + 3112 * q^62 + 9824 * q^63 - 1536 * q^64 - 700 * q^65 + 6688 * q^66 + 6276 * q^67 + 5184 * q^68 + 1056 * q^69 + 360 * q^70 - 584 * q^71 + 4032 * q^72 + 3560 * q^73 + 5144 * q^74 - 48 * q^76 + 928 * q^77 - 1320 * q^78 - 4892 * q^79 - 160 * q^80 - 4024 * q^81 - 7920 * q^82 - 14816 * q^83 - 5608 * q^84 + 560 * q^85 - 2044 * q^86 + 11548 * q^87 - 352 * q^88 + 5044 * q^89 - 740 * q^90 + 568 * q^91 - 528 * q^92 + 8064 * q^93 + 960 * q^94 + 960 * q^95 - 128 * q^96 + 508 * q^97 + 2112 * q^98 + 6280 * q^99

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.g.a	$230$	$4$	230.g	23.c	$11$	$50$	$5$	$13.570$		None		✓			230.4.g.a	$2$	$0$	\(-10\)	\(-5\)	\(25\)	\(-19\)		$\mathrm{SU}(2)[C_{11}]$
230.4.g.b	$230$	$4$	230.g	23.c	$11$	$60$	$6$	$13.570$		None		✓			230.4.g.b	$2$	$0$	\(12\)	\(-3\)	\(-30\)	\(100\)		$\mathrm{SU}(2)[C_{11}]$
230.4.g.c	$230$	$4$	230.g	23.c	$11$	$60$	$6$	$13.570$		None		✓			230.4.g.c	$2$	$0$	\(12\)	\(5\)	\(30\)	\(-3\)		$\mathrm{SU}(2)[C_{11}]$
230.4.g.d	$230$	$4$	230.g	23.c	$11$	$70$	$7$	$13.570$		None		✓	✓		230.4.g.d	$2$	$0$	\(-14\)	\(3\)	\(-35\)	\(-78\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{4}^{\mathrm{old}}(230, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)