Space of modular forms of level 435, weight 3, and Character 435.b

• Label: 435.3.b
• Level: $435$
• Weight: $3$
• Character orbit: 435.b
• Rep. character: $\chi_{435}(434,\cdot)$
• Character field: $\Q$
• Dimension: $116$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	435.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 435 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(435, [\chi])\).

	Total	New	Old
Modular forms	124	124	0
Cusp forms	116	116	0
Eisenstein series	8	8	0

Trace form

\( 116 q - 232 q^{4} + 4 q^{6} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(435, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
435.3.b.a	$435$	$3$	435.b	435.b	$2$	$1$	$1$	$11.853$	\(\Q\)	\(\Q(\sqrt{-435}) \)	✓	✓			435.3.b.a	$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+4q^{4}-5q^{5}+9q^{9}-7q^{11}+\cdots\)
435.3.b.b	$435$	$3$	435.b	435.b	$2$	$1$	$1$	$11.853$	\(\Q\)	\(\Q(\sqrt{-435}) \)	✓	✓			435.3.b.a	$2$	$0$	\(0\)	\(-3\)	\(5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+4q^{4}+5q^{5}+9q^{9}+7q^{11}+\cdots\)
435.3.b.c	$435$	$3$	435.b	435.b	$2$	$1$	$1$	$11.853$	\(\Q\)	\(\Q(\sqrt{-435}) \)	✓	✓			435.3.b.a	$2$	$0$	\(0\)	\(3\)	\(-5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+4q^{4}-5q^{5}+9q^{9}+7q^{11}+\cdots\)
435.3.b.d	$435$	$3$	435.b	435.b	$2$	$1$	$1$	$11.853$	\(\Q\)	\(\Q(\sqrt{-435}) \)	✓	✓			435.3.b.a	$2$	$0$	\(0\)	\(3\)	\(5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+4q^{4}+5q^{5}+9q^{9}-7q^{11}+\cdots\)
435.3.b.e	$435$	$3$	435.b	435.b	$2$	$112$	$112$	$11.853$		None		✓	✓		435.3.b.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$