Space of modular forms of level 395, weight 3, and Character 395.c

• Label: 395.3.c
• Level: $395$
• Weight: $3$
• Character orbit: 395.c
• Rep. character: $\chi_{395}(394,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $4$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 395 = 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	395.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(395, [\chi])\).

	Total	New	Old
Modular forms	82	82	0
Cusp forms	78	78	0
Eisenstein series	4	4	0

Trace form

\( 78 q - 152 q^{4} - 2 q^{5} + 214 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(395, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
395.3.c.a	$395$	$3$	395.c	395.c	$2$	$4$	$4$	$10.763$	4.4.7988480.1	\(\Q(\sqrt{-395}) \)	✓	✓			395.3.c.a	$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}+4q^{4}-5q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
395.3.c.b	$395$	$3$	395.c	395.c	$2$	$4$	$4$	$10.763$	4.4.31600.1	\(\Q(\sqrt{-395}) \)	✓	✓			395.3.c.b	$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+4q^{4}+5q^{5}+(-2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
395.3.c.c	$395$	$3$	395.c	395.c	$2$	$10$	$10$	$10.763$	10.0.\(\cdots\).1	\(\Q(\sqrt{-79}) \)		✓			395.3.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+(-4+\beta _{2}+\beta _{4}+\beta _{6}+\beta _{9})q^{4}+\cdots\)
395.3.c.d	$395$	$3$	395.c	395.c	$2$	$60$	$60$	$10.763$		None		✓	✓		395.3.c.d	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$