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

• Label: 230.2.e
• Level: $230$
• Weight: $2$
• Character orbit: 230.e
• Rep. character: $\chi_{230}(137,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	80	24	56
Cusp forms	64	24	40
Eisenstein series	16	0	16

Trace form

24 * q + 8 * q^3 + 8 * q^6 + 8 * q^12 - 16 * q^13 - 24 * q^16 - 16 * q^18 - 8 * q^23 + 8 * q^26 - 16 * q^27 - 24 * q^31 + 8 * q^35 + 32 * q^36 + 24 * q^41 + 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^50 - 16 * q^52 + 32 * q^62 - 24 * q^70 - 104 * q^71 - 16 * q^72 + 88 * q^73 - 8 * q^75 + 24 * q^77 - 40 * q^78 - 40 * q^81 - 40 * q^82 + 56 * q^85 - 40 * q^87 - 8 * q^92 - 56 * q^93 - 96 * q^95 - 8 * q^96 + 64 * q^98

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.e.a	$230$	$2$	230.e	115.e	$4$	$8$	$4$	$1.837$	8.0.110166016.2	None		✓			230.2.e.a	$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.b	$230$	$2$	230.e	115.e	$4$	$8$	$4$	$1.837$	8.0.110166016.2	None		✓			230.2.e.a	$2$	$0$	\(0\)	\(-4\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.c	$230$	$2$	230.e	115.e	$4$	$8$	$4$	$1.837$	\(\Q(\zeta_{16})\)	None		✓			230.2.e.c	$4$	$0$	\(0\)	\(16\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}^{6}q^{2}+(2+2\zeta_{16}^{4})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)

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

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