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 + 44 * q^16 - 20 * q^20 - 12 * q^24 + 24 * q^25 - 12 * q^29 - 16 * q^30 - 32 * q^34 - 4 * q^35 + 36 * q^36 - 8 * q^45 - 32 * q^49 - 16 * q^51 - 4 * q^54 - 40 * q^59 - 12 * q^64 + 4 * q^65 + 8 * q^71 - 40 * q^74 - 72 * q^80 + 32 * q^81 - 40 * q^86 - 16 * q^91 - 88 * q^94 - 28 * q^96

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	$2$	$0$	\(-4\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{2}+q^{3}+2 q^{4}+(i+2)q^{5}+\cdots\)
435.2.f.b	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.b	$2$	$1$	\(-2\)	\(-2\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{3}-q^{4}+(\beta-1)q^{5}+q^{6}+\cdots\)
435.2.f.c	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.b	$2$	$0$	\(2\)	\(2\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{3}-q^{4}+(\beta-1)q^{5}+q^{6}+\cdots\)
435.2.f.d	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.f.a	$2$	$0$	\(4\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{2}-q^{3}+2 q^{4}+(i+2)q^{5}+\cdots\)
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

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