Space of modular forms of level 1092, weight 2, and Character 1092.bw

• Label: 1092.2.bw
• Level: $1092$
• Weight: $2$
• Character orbit: 1092.bw
• Rep. character: $\chi_{1092}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $448$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1092.bw (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(448\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1092, [\chi])\).

	Total	New	Old
Modular forms	472	64	408
Cusp forms	424	64	360
Eisenstein series	48	0	48

Trace form

64 * q + 4 * q^7 + 4 * q^9 + 12 * q^15 + 10 * q^21 - 36 * q^25 - 12 * q^31 - 32 * q^43 - 54 * q^45 - 28 * q^49 - 8 * q^51 + 56 * q^57 + 72 * q^61 - 10 * q^63 + 48 * q^73 - 60 * q^75 + 24 * q^79 - 4 * q^81 + 32 * q^85 - 48 * q^87 + 8 * q^91 + 10 * q^93 + 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1092, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1092.2.bw.a	$1092$	$2$	1092.bw	21.g	$6$	$64$	$32$	$8.720$		None		✓	✓	✓	1092.2.bw.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1092, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1092, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)