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

• Label: 230.2.b
• Level: $230$
• Weight: $2$
• Character orbit: 230.b
• Rep. character: $\chi_{230}(139,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	40	12	28
Cusp forms	32	12	20
Eisenstein series	8	0	8

Trace form

12 * q - 12 * q^4 + 4 * q^6 - 8 * q^9 - 8 * q^11 - 16 * q^15 + 12 * q^16 + 16 * q^19 - 4 * q^24 + 8 * q^25 + 4 * q^26 + 8 * q^29 - 12 * q^31 - 16 * q^35 + 8 * q^36 - 8 * q^39 + 28 * q^41 + 8 * q^44 - 16 * q^45 + 4 * q^46 - 8 * q^49 - 12 * q^50 + 24 * q^51 - 16 * q^54 - 8 * q^55 - 8 * q^59 + 16 * q^60 + 16 * q^61 - 12 * q^64 - 16 * q^65 + 8 * q^66 - 8 * q^69 + 20 * q^70 + 44 * q^71 - 32 * q^75 - 16 * q^76 + 16 * q^79 + 28 * q^81 - 24 * q^85 - 40 * q^86 - 48 * q^89 - 24 * q^90 - 32 * q^91 - 24 * q^94 + 48 * q^95 + 4 * q^96 + 32 * 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.b.a	$230$	$2$	230.b	5.b	$2$	$4$	$4$	$1.837$	\(\Q(i, \sqrt{5})\)	None		✓			230.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+2\beta _{2})q^{5}+\cdots\)
230.2.b.b	$230$	$2$	230.b	5.b	$2$	$8$	$8$	$1.837$	8.0.\(\cdots\).3	None		✓	✓		230.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{5})q^{3}-q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)

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

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