Space of modular forms of level 363, weight 2, and Character 363.i

• Label: 363.2.i
• Level: $363$
• Weight: $2$
• Character orbit: 363.i
• Rep. character: $\chi_{363}(34,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $220$
• Newform subspaces: $2$
• Sturm bound: $88$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(88\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(363, [\chi])\).

	Total	New	Old
Modular forms	460	220	240
Cusp forms	420	220	200
Eisenstein series	40	0	40

Trace form

220 * q - 4 * q^2 - 26 * q^4 - 4 * q^5 - 2 * q^6 - 12 * q^7 - 12 * q^8 + 220 * q^9 + 6 * q^10 + 10 * q^11 - 8 * q^12 + 32 * q^13 + 24 * q^14 - 8 * q^15 - 42 * q^16 - 16 * q^17 - 4 * q^18 - 20 * q^19 - 36 * q^20 - 4 * q^21 + 10 * q^22 + 16 * q^23 - 18 * q^24 - 50 * q^25 - 28 * q^26 - 52 * q^28 - 24 * q^29 - 20 * q^30 + 2 * q^31 - 68 * q^32 - 10 * q^33 - 40 * q^34 - 40 * q^35 - 26 * q^36 + 26 * q^37 - 56 * q^38 - 16 * q^39 + 36 * q^40 - 40 * q^41 - 16 * q^42 - 44 * q^43 - 54 * q^44 - 4 * q^45 - 80 * q^46 - 48 * q^47 - 32 * q^48 - 34 * q^49 + 172 * q^50 - 20 * q^51 + 54 * q^52 + 76 * q^53 - 2 * q^54 + 24 * q^55 + 70 * q^56 - 20 * q^57 + 2 * q^58 - 36 * q^59 - 28 * q^60 - 68 * q^61 + 22 * q^62 - 12 * q^63 - 82 * q^64 - 22 * q^65 - 32 * q^66 + 58 * q^67 - 128 * q^68 - 12 * q^69 - 64 * q^70 + 36 * q^71 - 12 * q^72 - 38 * q^73 - 120 * q^74 - 24 * q^75 + 102 * q^76 - 92 * q^77 + 78 * q^78 + 56 * q^79 - 152 * q^80 + 220 * q^81 - 48 * q^82 - 96 * q^83 - 60 * q^84 - 24 * q^85 - 100 * q^86 - 36 * q^87 - 118 * q^88 + 20 * q^89 + 6 * q^90 - 6 * q^91 + 92 * q^92 - 32 * q^93 + 200 * q^94 - 120 * q^95 + 74 * q^96 - 10 * q^97 - 4 * q^98 + 10 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(363, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
363.2.i.a	$363$	$2$	363.i	121.e	$11$	$110$	$11$	$2.899$		None		✓			363.2.i.a	$2$	$0$	\(-3\)	\(110\)	\(-6\)	\(-8\)		$\mathrm{SU}(2)[C_{11}]$
363.2.i.b	$363$	$2$	363.i	121.e	$11$	$110$	$11$	$2.899$		None		✓			363.2.i.b	$2$	$0$	\(-1\)	\(-110\)	\(2\)	\(-4\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

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