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

• Label: 363.2.e
• Level: $363$
• Weight: $2$
• Character orbit: 363.e
• Rep. character: $\chi_{363}(124,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $72$
• Newform subspaces: $14$
• Sturm bound: $88$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(88\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	224	72	152
Cusp forms	128	72	56
Eisenstein series	96	0	96

Trace form

72 * q + 4 * q^2 - 14 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 8 * q^8 - 18 * q^9 - 4 * q^10 + 8 * q^12 + 2 * q^13 + 6 * q^14 - 2 * q^15 - 22 * q^16 - 14 * q^17 - 6 * q^18 + 20 * q^19 + 2 * q^20 - 16 * q^21 - 4 * q^23 - 12 * q^24 - 20 * q^25 + 2 * q^26 + 12 * q^28 + 4 * q^29 + 8 * q^31 + 48 * q^32 - 56 * q^34 - 14 * q^36 - 2 * q^37 + 14 * q^38 + 16 * q^39 - 4 * q^40 - 20 * q^41 + 14 * q^42 - 16 * q^43 + 4 * q^45 - 10 * q^46 - 6 * q^47 - 8 * q^48 - 16 * q^49 - 18 * q^50 - 10 * q^52 - 6 * q^53 - 8 * q^54 - 108 * q^56 + 44 * q^58 + 46 * q^59 + 12 * q^60 + 18 * q^61 + 28 * q^62 + 2 * q^63 + 2 * q^64 + 28 * q^65 - 44 * q^67 + 28 * q^68 + 10 * q^69 + 34 * q^70 + 32 * q^71 + 2 * q^72 - 20 * q^73 + 30 * q^74 - 40 * q^76 - 64 * q^78 + 6 * q^79 + 14 * q^80 - 18 * q^81 + 46 * q^82 - 34 * q^83 + 2 * q^85 + 24 * q^86 - 24 * q^87 - 60 * q^89 - 4 * q^90 - 18 * q^91 + 22 * q^92 - 56 * q^93 - 18 * q^94 - 30 * q^95 + 8 * q^96 + 10 * q^97 - 40 * q^98

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.e.a	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None		✓			363.2.a.g	$4$	$1$	\(-5\)	\(-1\)	\(-2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.b	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.e.b	$2$	$0$	\(-4\)	\(1\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.c	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.e.a	$2$	$0$	\(-2\)	\(-1\)	\(4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
363.2.e.d	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None		✓			363.2.a.a	$4$	$0$	\(-2\)	\(1\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.e	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.a.a	$4$	$0$	\(-1\)	\(1\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.f	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.e.b	$2$	$0$	\(1\)	\(1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.g	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.a.a	$4$	$0$	\(1\)	\(1\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.h	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.e.a	$2$	$0$	\(2\)	\(-1\)	\(4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
363.2.e.i	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None		✓			363.2.a.a	$4$	$0$	\(2\)	\(1\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.j	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.e.a	$2$	$0$	\(3\)	\(-1\)	\(-1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
363.2.e.k	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None					33.2.e.b	$2$	$0$	\(4\)	\(1\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.l	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	\(\Q(\zeta_{10})\)	None		✓			363.2.a.g	$4$	$0$	\(5\)	\(-1\)	\(-2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.m	$363$	$2$	363.e	11.c	$5$	$8$	$2$	$2.899$	8.0.324000000.3	None		✓			363.2.a.f	$8$	$0$	\(0\)	\(2\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(3+3\beta _{2}+\cdots)q^{5}+\cdots\)
363.2.e.n	$363$	$2$	363.e	11.c	$5$	$16$	$4$	$2.899$	16.0.\(\cdots\).3	None		✓	✓		363.2.a.j	$8$	$0$	\(0\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{12}q^{2}+\beta _{4}q^{3}+(\beta _{3}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(363, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)