Space of modular forms of level 231, weight 2, and Character 231.j

• Label: 231.2.j
• Level: $231$
• Weight: $2$
• Character orbit: 231.j
• Rep. character: $\chi_{231}(64,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

	Total	New	Old
Modular forms	144	48	96
Cusp forms	112	48	64
Eisenstein series	32	0	32

Trace form

48 * q + 4 * q^2 - 8 * q^4 + 4 * q^7 - 8 * q^8 - 12 * q^9 + 16 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 6 * q^14 + 8 * q^15 - 44 * q^16 + 8 * q^17 - 6 * q^18 + 8 * q^19 - 60 * q^20 - 16 * q^21 + 36 * q^22 - 16 * q^23 - 36 * q^25 - 52 * q^26 + 2 * q^28 + 16 * q^29 - 8 * q^30 + 20 * q^31 + 88 * q^32 + 8 * q^33 + 56 * q^34 - 8 * q^36 - 28 * q^37 + 4 * q^38 + 32 * q^39 + 4 * q^40 + 8 * q^41 - 48 * q^43 + 18 * q^44 - 6 * q^46 - 8 * q^47 - 16 * q^48 - 12 * q^49 - 64 * q^50 + 24 * q^51 - 68 * q^52 - 52 * q^53 + 36 * q^56 - 8 * q^57 + 42 * q^58 - 4 * q^59 - 36 * q^60 + 32 * q^62 + 4 * q^63 - 36 * q^64 + 40 * q^65 + 80 * q^67 + 88 * q^68 - 12 * q^69 + 20 * q^70 + 4 * q^71 + 2 * q^72 + 8 * q^73 - 28 * q^74 - 32 * q^75 - 16 * q^76 + 16 * q^77 - 8 * q^78 + 36 * q^79 + 176 * q^80 - 12 * q^81 + 4 * q^82 - 88 * q^83 + 12 * q^84 - 12 * q^85 + 102 * q^86 + 40 * q^87 + 84 * q^88 - 64 * q^89 - 24 * q^90 + 10 * q^92 - 20 * q^93 - 20 * q^94 - 128 * q^95 - 60 * q^96 + 28 * q^97 + 4 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.2.j.a	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	\(\Q(\zeta_{10})\)	None		✓			231.2.j.a	$2$	$0$	\(-4\)	\(1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
231.2.j.b	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	\(\Q(\zeta_{10})\)	None		✓			231.2.j.b	$2$	$0$	\(-2\)	\(1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
231.2.j.c	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	\(\Q(\zeta_{10})\)	None		✓			231.2.j.c	$2$	$0$	\(1\)	\(1\)	\(7\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
231.2.j.d	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	\(\Q(\zeta_{10})\)	None		✓			231.2.j.d	$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
231.2.j.e	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	\(\Q(\zeta_{10})\)	None		✓			231.2.j.e	$2$	$0$	\(5\)	\(1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
231.2.j.f	$231$	$2$	231.j	11.c	$5$	$8$	$2$	$1.845$	8.0.13140625.1	None		✓			231.2.j.f	$2$	$0$	\(2\)	\(2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
231.2.j.g	$231$	$2$	231.j	11.c	$5$	$20$	$5$	$1.845$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		231.2.j.g	$2$	$0$	\(0\)	\(-5\)	\(-5\)	\(5\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}-\beta _{4}q^{3}+(\beta _{3}-\beta _{6}-\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)