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

\( 28 q - 2 q^{3} + 24 q^{4} + 6 q^{9} + O(q^{10}) \)

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

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

\( S_{2}^{\mathrm{old}}(363, [\chi]) \cong \)