Space of modular forms of level 231, weight 4, and Character 231.i

• Label: 231.4.i
• Level: $231$
• Weight: $4$
• Character orbit: 231.i
• Rep. character: $\chi_{231}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(231, [\chi])\).

	Total	New	Old
Modular forms	200	80	120
Cusp forms	184	80	104
Eisenstein series	16	0	16

Trace form

80 * q - 12 * q^3 - 160 * q^4 + 44 * q^7 - 168 * q^8 - 360 * q^9 + 12 * q^10 - 144 * q^12 - 200 * q^13 + 340 * q^14 - 584 * q^16 + 4 * q^19 - 1312 * q^20 - 216 * q^21 - 176 * q^23 - 1128 * q^25 + 868 * q^26 + 216 * q^27 + 768 * q^28 - 384 * q^29 + 336 * q^30 - 420 * q^31 + 812 * q^32 - 132 * q^33 + 1312 * q^34 - 1032 * q^35 + 2880 * q^36 - 728 * q^37 - 204 * q^38 - 756 * q^39 + 1164 * q^40 - 256 * q^41 - 612 * q^42 + 408 * q^43 - 616 * q^44 - 520 * q^46 - 224 * q^47 + 3744 * q^48 - 508 * q^49 + 2720 * q^50 - 120 * q^51 + 2596 * q^52 - 528 * q^53 + 1760 * q^55 + 1680 * q^56 - 840 * q^57 - 1144 * q^58 - 544 * q^59 - 1032 * q^60 + 1336 * q^61 - 200 * q^62 - 36 * q^63 + 9024 * q^64 + 800 * q^65 - 528 * q^66 - 1108 * q^67 - 3084 * q^68 + 2808 * q^69 - 2880 * q^70 + 3488 * q^71 + 756 * q^72 + 340 * q^73 - 96 * q^74 - 1788 * q^75 - 2512 * q^76 + 176 * q^77 - 2472 * q^78 + 2356 * q^79 + 1264 * q^80 - 3240 * q^81 - 5648 * q^82 - 9760 * q^83 - 1200 * q^84 - 4224 * q^85 - 1836 * q^86 + 936 * q^87 + 396 * q^88 + 1088 * q^89 - 216 * q^90 + 3268 * q^91 + 4624 * q^92 - 252 * q^93 + 2964 * q^94 - 3640 * q^95 - 2580 * q^96 + 1128 * q^97 + 2484 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(231, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.4.i.a	$231$	$4$	231.i	7.c	$3$	$16$	$8$	$13.629$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			231.4.i.a	$2$	$0$	\(4\)	\(24\)	\(-20\)	\(18\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{2}+3\beta _{4}q^{3}+\cdots\)
231.4.i.b	$231$	$4$	231.i	7.c	$3$	$20$	$10$	$13.629$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			231.4.i.b	$2$	$0$	\(-4\)	\(30\)	\(20\)	\(10\)	$2^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
231.4.i.c	$231$	$4$	231.i	7.c	$3$	$20$	$10$	$13.629$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			231.4.i.c	$2$	$0$	\(4\)	\(-30\)	\(20\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-3+3\beta _{4})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
231.4.i.d	$231$	$4$	231.i	7.c	$3$	$24$	$12$	$13.629$		None		✓	✓		231.4.i.d	$2$	$0$	\(-4\)	\(-36\)	\(-20\)	\(12\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)