Space of modular forms of level 228, weight 3, and Character 228.l

• Label: 228.3.l
• Level: $228$
• Weight: $3$
• Character orbit: 228.l
• Rep. character: $\chi_{228}(145,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).

	Total	New	Old
Modular forms	172	12	160
Cusp forms	148	12	136
Eisenstein series	24	0	24

Trace form

12 * q + 2 * q^5 + 20 * q^7 + 18 * q^9 - 4 * q^11 + 6 * q^13 - 18 * q^15 - 4 * q^17 + 40 * q^19 + 14 * q^23 + 26 * q^25 + 156 * q^29 + 54 * q^33 + 82 * q^35 - 72 * q^39 - 72 * q^41 + 6 * q^43 + 12 * q^45 - 28 * q^47 - 240 * q^49 - 6 * q^53 - 124 * q^55 + 96 * q^57 - 318 * q^59 + 38 * q^61 + 30 * q^63 + 282 * q^67 - 54 * q^73 - 428 * q^77 - 42 * q^79 - 54 * q^81 + 8 * q^83 - 136 * q^85 - 144 * q^87 - 6 * q^89 - 18 * q^91 - 60 * q^93 + 50 * q^95 - 144 * q^97 - 6 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(228, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
228.3.l.a	$228$	$3$	228.l	19.d	$6$	$2$	$1$	$6.213$	\(\Q(\sqrt{-3}) \)	None		✓			228.3.l.a	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(-6+6\zeta_{6})q^{5}-5q^{7}+\cdots\)
228.3.l.b	$228$	$3$	228.l	19.d	$6$	$2$	$1$	$6.213$	\(\Q(\sqrt{-3}) \)	None		✓			228.3.l.b	$2$	$0$	\(0\)	\(3\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
228.3.l.c	$228$	$3$	228.l	19.d	$6$	$2$	$1$	$6.213$	\(\Q(\sqrt{-3}) \)	None		✓			228.3.l.c	$2$	$0$	\(0\)	\(3\)	\(2\)	\(22\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+11q^{7}+\cdots\)
228.3.l.d	$228$	$3$	228.l	19.d	$6$	$6$	$3$	$6.213$	6.0.954288.1	None		✓	✓		228.3.l.d	$2$	$0$	\(0\)	\(-9\)	\(4\)	\(10\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{2})q^{3}+(2-2\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(228, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)