Space of modular forms of level 920, weight 2, and Character 920.y

• Label: 920.2.y
• Level: $920$
• Weight: $2$
• Character orbit: 920.y
• Rep. character: $\chi_{920}(41,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $240$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.y (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

	Total	New	Old
Modular forms	1520	240	1280
Cusp forms	1360	240	1120
Eisenstein series	160	0	160

Trace form

240 * q - 2 * q^5 - 28 * q^9 - 4 * q^11 - 8 * q^17 - 4 * q^19 - 8 * q^21 - 4 * q^23 - 24 * q^25 + 12 * q^29 - 16 * q^31 - 24 * q^33 + 18 * q^35 - 20 * q^37 + 12 * q^39 + 44 * q^41 + 84 * q^43 + 72 * q^45 - 8 * q^47 + 26 * q^49 + 72 * q^51 + 8 * q^53 + 36 * q^55 - 32 * q^57 + 42 * q^59 - 28 * q^61 - 24 * q^63 + 4 * q^65 - 4 * q^67 + 16 * q^71 - 24 * q^73 + 48 * q^77 - 116 * q^79 - 56 * q^81 - 72 * q^83 - 348 * q^87 - 108 * q^89 - 40 * q^91 + 32 * q^93 - 132 * q^97 - 344 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
920.2.y.a	$920$	$2$	920.y	23.c	$11$	$50$	$5$	$7.346$		None		✓			920.2.y.a	$2$	$0$	\(0\)	\(1\)	\(5\)	\(9\)		$\mathrm{SU}(2)[C_{11}]$
920.2.y.b	$920$	$2$	920.y	23.c	$11$	$60$	$6$	$7.346$		None		✓			920.2.y.b	$2$	$0$	\(0\)	\(-1\)	\(-6\)	\(18\)		$\mathrm{SU}(2)[C_{11}]$
920.2.y.c	$920$	$2$	920.y	23.c	$11$	$60$	$6$	$7.346$		None		✓			920.2.y.c	$2$	$0$	\(0\)	\(-1\)	\(6\)	\(-7\)		$\mathrm{SU}(2)[C_{11}]$
920.2.y.d	$920$	$2$	920.y	23.c	$11$	$70$	$7$	$7.346$		None		✓	✓		920.2.y.d	$2$	$0$	\(0\)	\(1\)	\(-7\)	\(-20\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)