Space of modular forms of level 230, weight 2, and Character 230.g

• Label: 230.2.g
• Level: $230$
• Weight: $2$
• Character orbit: 230.g
• Rep. character: $\chi_{230}(31,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $72$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(72\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(230, [\chi])\).

	Total	New	Old
Modular forms	400	80	320
Cusp forms	320	80	240
Eisenstein series	80	0	80

Trace form

80 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^9 + 2 * q^10 + 12 * q^11 + 8 * q^13 + 8 * q^14 - 8 * q^16 - 20 * q^17 + 16 * q^18 - 32 * q^19 + 2 * q^20 - 84 * q^21 - 40 * q^22 + 24 * q^23 + 4 * q^24 - 8 * q^25 - 16 * q^26 - 84 * q^27 - 4 * q^29 + 8 * q^30 - 16 * q^31 + 72 * q^33 + 24 * q^34 - 14 * q^35 - 4 * q^36 + 28 * q^37 + 28 * q^38 + 28 * q^39 + 2 * q^40 + 24 * q^41 + 64 * q^42 - 68 * q^43 + 12 * q^44 - 40 * q^45 + 24 * q^46 + 72 * q^47 - 22 * q^49 + 16 * q^51 + 8 * q^52 + 32 * q^53 + 42 * q^54 - 20 * q^55 - 14 * q^56 - 4 * q^57 - 32 * q^58 - 22 * q^59 - 36 * q^61 - 100 * q^62 - 100 * q^63 - 8 * q^64 + 20 * q^65 - 32 * q^66 - 44 * q^67 - 64 * q^68 + 96 * q^69 + 12 * q^70 + 84 * q^71 - 72 * q^72 - 16 * q^73 - 44 * q^74 + 12 * q^76 - 116 * q^77 - 92 * q^78 - 76 * q^79 + 2 * q^80 - 56 * q^82 - 100 * q^83 + 26 * q^84 + 4 * q^85 - 2 * q^86 - 28 * q^87 + 4 * q^88 + 28 * q^89 + 26 * q^90 + 96 * q^91 + 24 * q^92 + 88 * q^93 + 40 * q^94 + 32 * q^95 + 4 * q^96 + 44 * q^97 + 32 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(230, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
230.2.g.a	$230$	$2$	230.g	23.c	$11$	$10$	$1$	$1.837$	\(\Q(\zeta_{22})\)	None		✓			230.2.g.a	$2$	$0$	\(-1\)	\(3\)	\(-1\)	\(-15\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\zeta_{22}^{4}q^{2}+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\cdots)q^{3}+\cdots\)
230.2.g.b	$230$	$2$	230.g	23.c	$11$	$20$	$2$	$1.837$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			230.2.g.b	$2$	$0$	\(2\)	\(-3\)	\(-2\)	\(19\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{2}+\beta _{5}-\beta _{13}+\beta _{18}+\cdots)q^{3}+\cdots\)
230.2.g.c	$230$	$2$	230.g	23.c	$11$	$20$	$2$	$1.837$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			230.2.g.c	$2$	$0$	\(2\)	\(1\)	\(2\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{3}q^{2}+(\beta _{5}+\beta _{18})q^{3}+\beta _{12}q^{4}+\cdots\)
230.2.g.d	$230$	$2$	230.g	23.c	$11$	$30$	$3$	$1.837$		None		✓	✓		230.2.g.d	$2$	$0$	\(-3\)	\(-1\)	\(3\)	\(8\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

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