Space of modular forms of level 928, weight 2, and Character 928.k

• Label: 928.2.k
• Level: $928$
• Weight: $2$
• Character orbit: 928.k
• Rep. character: $\chi_{928}(191,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $8$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	928.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(928, [\chi])\).

	Total	New	Old
Modular forms	256	60	196
Cusp forms	224	60	164
Eisenstein series	32	0	32

Trace form

\( 60 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(928, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
928.2.k.a	$928$	$2$	928.k	116.e	$4$	$2$	$1$	$7.410$	\(\Q(\sqrt{-1}) \)	None		✓			928.2.k.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}-2iq^{7}+iq^{9}+(-1+\cdots)q^{11}+\cdots\)
928.2.k.b	$928$	$2$	928.k	116.e	$4$	$2$	$1$	$7.410$	\(\Q(\sqrt{-1}) \)	None		✓			928.2.k.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+2iq^{7}+iq^{9}+(1-i)q^{11}+\cdots\)
928.2.k.c	$928$	$2$	928.k	116.e	$4$	$4$	$2$	$7.410$	\(\Q(\zeta_{8})\)	None		✓			928.2.k.c	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
928.2.k.d	$928$	$2$	928.k	116.e	$4$	$4$	$2$	$7.410$	\(\Q(\zeta_{8})\)	None		✓			928.2.k.c	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
928.2.k.e	$928$	$2$	928.k	116.e	$4$	$10$	$5$	$7.410$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			928.2.k.e	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{3}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\)
928.2.k.f	$928$	$2$	928.k	116.e	$4$	$10$	$5$	$7.410$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			928.2.k.e	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{3}+\beta _{7}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\)
928.2.k.g	$928$	$2$	928.k	116.e	$4$	$14$	$7$	$7.410$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			928.2.k.g	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{3}+(-\beta _{1}+\beta _{7}-\beta _{9})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
928.2.k.h	$928$	$2$	928.k	116.e	$4$	$14$	$7$	$7.410$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			928.2.k.g	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{3}+(-\beta _{1}+\beta _{7}-\beta _{9})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(928, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(928, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 2}\)