Space of modular forms of level 1188, weight 3, and Character 1188.e

• Label: 1188.3.e
• Level: $1188$
• Weight: $3$
• Character orbit: 1188.e
• Rep. character: $\chi_{1188}(485,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $4$
• Sturm bound: $648$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1188 = 2^{2} \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1188.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(648\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1188, [\chi])\).

	Total	New	Old
Modular forms	450	26	424
Cusp forms	414	26	388
Eisenstein series	36	0	36

Trace form

\( 26 q + 14 q^{7} - 98 q^{13} + 22 q^{19} + 18 q^{25} - 68 q^{31} - 2 q^{37} + 84 q^{43} + 240 q^{49} - 234 q^{61} + 106 q^{67} - 118 q^{73} - 118 q^{79} - 36 q^{85} - 210 q^{91} + 270 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1188, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1188.3.e.a	$1188$	$3$	1188.e	3.b	$2$	$2$	$2$	$32.371$	\(\Q(\sqrt{-11}) \)	None		✓			1188.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-22\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{5}-11q^{7}-\beta q^{11}+q^{13}+2\beta q^{17}+\cdots\)
1188.3.e.b	$1188$	$3$	1188.e	3.b	$2$	$4$	$4$	$32.371$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		✓			1188.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}-\beta _{3})q^{5}+2q^{7}+\beta _{3}q^{11}+(-5+\cdots)q^{13}+\cdots\)
1188.3.e.c	$1188$	$3$	1188.e	3.b	$2$	$8$	$8$	$32.371$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			1188.3.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}\cdot 3^{2}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}+(1+\beta _{4})q^{7}-\beta _{1}q^{11}+(-2+\cdots)q^{13}+\cdots\)
1188.3.e.d	$1188$	$3$	1188.e	3.b	$2$	$12$	$12$	$32.371$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		1188.3.e.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(2+\beta _{2})q^{7}-\beta _{6}q^{11}+(-5+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1188, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1188, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(594, [\chi])\)\(^{\oplus 2}\)