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

• Label: 363.2.d
• Level: $363$
• Weight: $2$
• Character orbit: 363.d
• Rep. character: $\chi_{363}(362,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $88$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(88\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	56	44	12
Cusp forms	32	28	4
Eisenstein series	24	16	8

Trace form

28 * q - 2 * q^3 + 24 * q^4 + 6 * q^9 - 12 * q^12 - 14 * q^15 - 8 * q^16 + 28 * q^25 + 4 * q^27 - 16 * q^31 - 16 * q^34 - 16 * q^36 + 12 * q^37 + 40 * q^42 - 30 * q^45 - 24 * q^48 + 20 * q^49 + 8 * q^58 - 24 * q^60 - 36 * q^64 + 8 * q^67 - 6 * q^69 - 44 * q^70 - 24 * q^75 - 8 * q^78 - 10 * q^81 + 4 * q^82 - 44 * q^91 - 2 * q^93 + 12 * q^97

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.d.a	$363$	$2$	363.d	33.d	$2$	$2$	$2$	$2.899$	\(\Q(\sqrt{-2}) \)	None		✓			363.2.d.a	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
363.2.d.b	$363$	$2$	363.d	33.d	$2$	$2$	$2$	$2.899$	\(\Q(\sqrt{-2}) \)	None		✓			363.2.d.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
363.2.d.c	$363$	$2$	363.d	33.d	$2$	$4$	$4$	$2.899$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			363.2.d.c	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+\cdots\)
363.2.d.d	$363$	$2$	363.d	33.d	$2$	$4$	$4$	$2.899$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-3}) \)		✓			363.2.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$11$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}-2q^{4}-\beta _{2}q^{7}+3q^{9}+2\beta _{1}q^{12}+\cdots\)
363.2.d.e	$363$	$2$	363.d	33.d	$2$	$8$	$8$	$2.899$	8.0.3588489216.5	None		✓			363.2.d.e	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{7})q^{3}+(2-\beta _{4}-\beta _{7})q^{4}+\cdots\)
363.2.d.f	$363$	$2$	363.d	33.d	$2$	$8$	$8$	$2.899$	\(\Q(\zeta_{20})\)	None					33.2.f.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{2}+(\beta_{5}+\beta_{3}-\beta_1+1)q^{3}+\cdots\)

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

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