Space of modular forms of level 726, weight 2, and Character 726.i

• Label: 726.2.i
• Level: $726$
• Weight: $2$
• Character orbit: 726.i
• Rep. character: $\chi_{726}(67,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $220$
• Newform subspaces: $4$
• Sturm bound: $264$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(264\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(726, [\chi])\).

	Total	New	Old
Modular forms	1360	220	1140
Cusp forms	1280	220	1060
Eisenstein series	80	0	80

Trace form

220 * q - 22 * q^4 + 8 * q^5 + 2 * q^6 + 12 * q^7 + 220 * q^9 - 14 * q^10 - 32 * q^11 - 68 * q^13 - 28 * q^14 + 12 * q^15 - 22 * q^16 + 24 * q^17 + 20 * q^19 + 8 * q^20 + 4 * q^21 - 34 * q^22 + 16 * q^23 + 2 * q^24 + 6 * q^25 + 8 * q^26 + 12 * q^28 + 8 * q^29 + 12 * q^30 - 16 * q^31 + 10 * q^33 + 8 * q^34 + 48 * q^35 - 22 * q^36 - 92 * q^37 + 8 * q^38 + 8 * q^39 - 36 * q^40 + 40 * q^41 + 4 * q^42 + 28 * q^43 + 12 * q^44 + 8 * q^45 + 32 * q^46 + 56 * q^47 - 66 * q^49 + 16 * q^50 + 28 * q^51 + 20 * q^52 - 4 * q^53 + 2 * q^54 + 28 * q^55 + 16 * q^56 + 28 * q^57 - 32 * q^58 + 40 * q^59 + 12 * q^60 + 76 * q^61 + 48 * q^62 + 12 * q^63 - 22 * q^64 - 20 * q^65 + 8 * q^66 - 156 * q^67 + 24 * q^68 + 24 * q^69 - 4 * q^70 - 16 * q^71 + 40 * q^73 + 24 * q^74 + 16 * q^75 - 24 * q^76 + 88 * q^77 - 72 * q^79 + 8 * q^80 + 220 * q^81 - 4 * q^82 + 88 * q^83 + 4 * q^84 - 80 * q^85 + 40 * q^86 + 20 * q^87 + 10 * q^88 - 24 * q^89 - 14 * q^90 - 52 * q^91 - 28 * q^92 + 16 * q^93 - 296 * q^94 + 112 * q^95 + 2 * q^96 - 56 * q^97 + 48 * q^98 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(726, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
726.2.i.a	$726$	$2$	726.i	121.e	$11$	$50$	$5$	$5.797$		None		✓			726.2.i.a	$2$	$0$	\(-5\)	\(50\)	\(10\)	\(9\)		$\mathrm{SU}(2)[C_{11}]$
726.2.i.b	$726$	$2$	726.i	121.e	$11$	$50$	$5$	$5.797$		None		✓			726.2.i.b	$2$	$0$	\(5\)	\(-50\)	\(0\)	\(-1\)		$\mathrm{SU}(2)[C_{11}]$
726.2.i.c	$726$	$2$	726.i	121.e	$11$	$60$	$6$	$5.797$		None		✓			726.2.i.c	$2$	$0$	\(-6\)	\(-60\)	\(-2\)	\(5\)		$\mathrm{SU}(2)[C_{11}]$
726.2.i.d	$726$	$2$	726.i	121.e	$11$	$60$	$6$	$5.797$		None		✓			726.2.i.d	$2$	$0$	\(6\)	\(60\)	\(0\)	\(-1\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(726, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(726, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)