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

• Label: 435.2.d
• Level: $435$
• Weight: $2$
• Character orbit: 435.d
• Rep. character: $\chi_{435}(376,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
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	20	44
Cusp forms	56	20	36
Eisenstein series	8	0	8

Trace form

20 * q - 28 * q^4 + 8 * q^7 - 20 * q^9 - 8 * q^13 + 28 * q^16 - 12 * q^22 - 8 * q^23 - 12 * q^24 + 20 * q^25 + 44 * q^28 + 16 * q^29 + 4 * q^30 - 16 * q^33 + 4 * q^34 + 8 * q^35 + 28 * q^36 - 40 * q^38 + 20 * q^42 + 28 * q^49 - 8 * q^51 - 20 * q^52 - 64 * q^53 - 8 * q^57 + 44 * q^58 - 24 * q^59 - 32 * q^62 - 8 * q^63 - 8 * q^64 - 48 * q^71 - 40 * q^74 + 52 * q^78 - 32 * q^80 + 20 * q^81 + 80 * q^82 + 80 * q^83 - 96 * q^86 - 8 * q^87 - 16 * q^88 + 32 * q^91 + 120 * q^92 - 24 * q^93 - 36 * q^94 + 64 * 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.d.a	$435$	$2$	435.d	29.b	$2$	$10$	$10$	$3.473$	10.0.\(\cdots\).1	None		✓			435.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)
435.2.d.b	$435$	$2$	435.d	29.b	$2$	$10$	$10$	$3.473$	10.0.\(\cdots\).1	None		✓			435.2.d.b	$2$	$0$	\(0\)	\(0\)	\(10\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)