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

• Label: 231.2.y
• Level: $231$
• Weight: $2$
• Character orbit: 231.y
• Rep. character: $\chi_{231}(4,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 2 \)
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	288	128	160
Cusp forms	224	128	96
Eisenstein series	64	0	64

Trace form

128 * q + 4 * q^2 + 20 * q^4 - 4 * q^5 - 8 * q^6 - 2 * q^7 + 16 * q^8 + 16 * q^9 - 36 * q^10 - 2 * q^11 - 16 * q^13 - 20 * q^14 - 12 * q^15 - 6 * q^18 + 8 * q^19 + 48 * q^20 - 52 * q^22 - 8 * q^23 + 30 * q^24 - 12 * q^25 + 8 * q^26 - 38 * q^28 - 56 * q^29 + 8 * q^30 + 6 * q^31 + 8 * q^32 - 6 * q^33 - 144 * q^34 + 36 * q^35 - 40 * q^36 - 32 * q^37 - 8 * q^38 + 42 * q^40 - 48 * q^41 - 2 * q^42 - 8 * q^43 - 26 * q^44 - 4 * q^45 - 38 * q^46 - 44 * q^47 + 66 * q^49 - 56 * q^50 + 12 * q^51 + 12 * q^52 - 52 * q^53 - 16 * q^54 - 56 * q^55 - 24 * q^56 - 16 * q^57 + 12 * q^58 + 8 * q^59 - 18 * q^61 + 96 * q^62 - 14 * q^63 - 96 * q^64 + 16 * q^65 - 12 * q^66 + 72 * q^67 - 56 * q^68 + 24 * q^69 + 58 * q^70 + 128 * q^71 + 2 * q^72 - 6 * q^73 + 4 * q^74 - 8 * q^75 + 272 * q^76 + 4 * q^77 + 120 * q^78 - 6 * q^79 - 88 * q^80 + 16 * q^81 + 128 * q^83 - 12 * q^84 + 172 * q^85 - 34 * q^86 - 100 * q^87 + 28 * q^88 + 72 * q^89 - 8 * q^90 + 300 * q^92 - 44 * q^93 - 52 * q^94 - 10 * q^95 + 4 * q^96 + 32 * q^97 - 240 * q^98 + 44 * 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.y.a	$231$	$2$	231.y	77.m	$15$	$64$	$8$	$1.845$		None		✓			231.2.y.a	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-1\)		$\mathrm{SU}(2)[C_{15}]$
231.2.y.b	$231$	$2$	231.y	77.m	$15$	$64$	$8$	$1.845$		None		✓			231.2.y.b	$4$	$0$	\(4\)	\(8\)	\(-4\)	\(-1\)		$\mathrm{SU}(2)[C_{15}]$

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

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