Space of modular forms of level 435, weight 2, and Character 435.f

• Label: 435.2.f
• Level: $435$
• Weight: $2$
• Character orbit: 435.f
• Rep. character: $\chi_{435}(289,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).

	Total	New	Old
Modular forms	64	32	32
Cusp forms	56	32	24
Eisenstein series	8	0	8

Trace form

\( 32 q + 36 q^{4} - 8 q^{5} - 4 q^{6} + 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
435.2.f.a	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.a	$2$	$0$	\(-4\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots\)
435.2.f.b	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.b	$2$	$1$	\(-2\)	\(-2\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\)
435.2.f.c	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.b	$2$	$0$	\(2\)	\(2\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\)
435.2.f.d	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.a	$2$	$0$	\(4\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}-q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots\)
435.2.f.e	$435$	$2$	435.f	145.d	$2$	$12$	$12$	$3.473$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			435.2.f.e	$2$	$0$	\(0\)	\(-12\)	\(-6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
435.2.f.f	$435$	$2$	435.f	145.d	$2$	$12$	$12$	$3.473$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			435.2.f.e	$2$	$0$	\(0\)	\(12\)	\(-6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)