Space of modular forms of level 1134, weight 2, and Character 1134.k

• Label: 1134.2.k
• Level: $1134$
• Weight: $2$
• Character orbit: 1134.k
• Rep. character: $\chi_{1134}(647,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1134, [\chi])\).

	Total	New	Old
Modular forms	480	64	416
Cusp forms	384	64	320
Eisenstein series	96	0	96

Trace form

64 * q + 32 * q^4 + 8 * q^7 - 32 * q^16 - 32 * q^25 + 4 * q^28 + 12 * q^31 + 4 * q^37 - 56 * q^43 + 12 * q^46 + 4 * q^49 - 12 * q^52 - 12 * q^58 + 96 * q^61 - 64 * q^64 + 20 * q^67 - 12 * q^70 + 72 * q^73 - 16 * q^79 + 96 * q^85 - 48 * q^91 - 72 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1134, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1134.2.k.a	$1134$	$2$	1134.k	21.g	$6$	$16$	$8$	$9.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					126.2.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{2}+\beta _{8}q^{4}+(\beta _{5}+\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)
1134.2.k.b	$1134$	$2$	1134.k	21.g	$6$	$16$	$8$	$9.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					126.2.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{2}+\beta _{8}q^{4}+(-\beta _{5}-\beta _{10}-\beta _{12}+\cdots)q^{5}+\cdots\)
1134.2.k.c	$1134$	$2$	1134.k	21.g	$6$	$16$	$8$	$9.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1134.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{9}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{12}+\cdots)q^{5}+\cdots\)
1134.2.k.d	$1134$	$2$	1134.k	21.g	$6$	$16$	$8$	$9.055$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1134.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{12}-\beta _{14}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)