Space of modular forms of level 352, weight 2, and Character 352.m

• Label: 352.2.m
• Level: $352$
• Weight: $2$
• Character orbit: 352.m
• Rep. character: $\chi_{352}(97,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

	Total	New	Old
Modular forms	224	48	176
Cusp forms	160	48	112
Eisenstein series	64	0	64

Trace form

\( 48 q - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
352.2.m.a	$352$	$2$	352.m	11.c	$5$	$4$	$1$	$2.811$	\(\Q(\zeta_{10})\)	None		✓			352.2.m.a	$2$	$1$	\(0\)	\(-2\)	\(-6\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
352.2.m.b	$352$	$2$	352.m	11.c	$5$	$4$	$1$	$2.811$	\(\Q(\zeta_{10})\)	None		✓			352.2.m.a	$2$	$0$	\(0\)	\(2\)	\(-6\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}+\zeta_{10}^{3})q^{3}+(-2-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
352.2.m.c	$352$	$2$	352.m	11.c	$5$	$8$	$2$	$2.811$	8.0.484000000.9	None		✓			352.2.m.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3}+\beta _{5})q^{5}+(\beta _{4}+\beta _{7})q^{7}+\cdots\)
352.2.m.d	$352$	$2$	352.m	11.c	$5$	$8$	$2$	$2.811$	8.0.484000000.6	None		✓			352.2.m.d	$4$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(1+\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots\)
352.2.m.e	$352$	$2$	352.m	11.c	$5$	$12$	$3$	$2.811$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			352.2.m.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{5}-\beta _{8})q^{3}+\beta _{9}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
352.2.m.f	$352$	$2$	352.m	11.c	$5$	$12$	$3$	$2.811$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			352.2.m.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}+\beta _{8})q^{3}+\beta _{9}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)