Space of modular forms of level 445, weight 2, and Character 445.c

• Label: 445.2.c
• Level: $445$
• Weight: $2$
• Character orbit: 445.c
• Rep. character: $\chi_{445}(444,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 445 = 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	445.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 445 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(445, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	44	44	0
Eisenstein series	4	4	0

Trace form

44 * q - 48 * q^4 - 2 * q^5 + 40 * q^9 + 6 * q^10 + 24 * q^16 + 22 * q^20 - 32 * q^21 - 6 * q^25 - 28 * q^34 - 68 * q^36 - 52 * q^39 - 34 * q^40 - 28 * q^44 - 16 * q^45 + 52 * q^49 - 6 * q^50 + 16 * q^55 - 56 * q^64 + 32 * q^69 + 16 * q^71 + 20 * q^79 - 102 * q^80 - 52 * q^81 + 156 * q^84 + 102 * q^85 - 8 * q^89 + 56 * q^90 + 28 * q^91 + 132 * q^94 - 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(445, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
445.2.c.a	$445$	$2$	445.c	445.c	$2$	$44$	$44$	$3.553$		None		✓	✓	✓	445.2.c.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$