Space of modular forms of level 968, weight 2, and Character 968.y

• Label: 968.2.y
• Level: $968$
• Weight: $2$
• Character orbit: 968.y
• Rep. character: $\chi_{968}(25,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $1320$
• Newform subspaces: $2$
• Sturm bound: $264$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.y (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{55})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(264\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

	Total	New	Old
Modular forms	5440	1320	4120
Cusp forms	5120	1320	3800
Eisenstein series	320	0	320

Trace form

1320 * q - 2 * q^3 - 4 * q^7 - 324 * q^9 - 3 * q^11 - 2 * q^13 + 6 * q^15 + 8 * q^17 + 11 * q^19 + 8 * q^21 + 12 * q^23 + 57 * q^25 + 7 * q^27 - 2 * q^31 - 13 * q^33 - 10 * q^35 - 8 * q^37 - 44 * q^39 - 20 * q^41 - 30 * q^43 - 28 * q^45 - 26 * q^47 + 23 * q^49 - 90 * q^51 + 2 * q^53 - 142 * q^55 - 24 * q^57 + 29 * q^59 + 18 * q^61 + 8 * q^63 + 20 * q^65 + 18 * q^67 + 48 * q^69 + 84 * q^71 + 8 * q^73 + q^75 - 118 * q^77 - 58 * q^79 - 355 * q^81 + 13 * q^83 - 36 * q^85 + 40 * q^87 + 46 * q^89 - 14 * q^91 - 2 * q^93 - 4 * q^95 + 3 * q^97 + 41 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
968.2.y.a	$968$	$2$	968.y	121.g	$55$	$640$	$16$	$7.730$		None		✓			968.2.y.a	$2$	$0$	\(0\)	\(8\)	\(-3\)	\(3\)		$\mathrm{SU}(2)[C_{55}]$
968.2.y.b	$968$	$2$	968.y	121.g	$55$	$680$	$17$	$7.730$		None		✓	✓		968.2.y.b	$2$	$0$	\(0\)	\(-10\)	\(3\)	\(-7\)		$\mathrm{SU}(2)[C_{55}]$

Decomposition of \(S_{2}^{\mathrm{old}}(968, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(968, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 2}\)