Space of modular forms of level 775, weight 2, and Character 775.f

• Label: 775.2.f
• Level: $775$
• Weight: $2$
• Character orbit: 775.f
• Rep. character: $\chi_{775}(557,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $92$
• Newform subspaces: $7$
• Sturm bound: $160$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(160\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

	Total	New	Old
Modular forms	172	100	72
Cusp forms	148	92	56
Eisenstein series	24	8	16

Trace form

\( 92 q + 4 q^{2} + 12 q^{7} - 10 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
775.2.f.a	$775$	$2$	775.f	155.f	$4$	$4$	$2$	$6.188$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
775.2.f.b	$775$	$2$	775.f	155.f	$4$	$4$	$2$	$6.188$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
775.2.f.c	$775$	$2$	775.f	155.f	$4$	$8$	$4$	$6.188$	8.0.3317760000.2	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}-\beta _{3}q^{3}-4\beta _{2}q^{4}-\beta _{7}q^{6}+\cdots\)
775.2.f.d	$775$	$2$	775.f	155.f	$4$	$8$	$4$	$6.188$	8.0.\(\cdots\).2	\(\Q(\sqrt{-155}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{3}q^{3}+2\beta _{4}q^{4}+(-3\beta _{4}-\beta _{7})q^{9}+\cdots\)
775.2.f.e	$775$	$2$	775.f	155.f	$4$	$12$	$6$	$6.188$	12.0.\(\cdots\).1	\(\Q(\sqrt{-31}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 5^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{4}q^{2}+(2\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\beta _{9}+\cdots)q^{7}+\cdots\)
775.2.f.f	$775$	$2$	775.f	155.f	$4$	$16$	$8$	$6.188$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(12\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{7}+\cdots)q^{6}+\cdots\)
775.2.f.g	$775$	$2$	775.f	155.f	$4$	$40$	$20$	$6.188$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \)