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

• Label: 435.2.c
• Level: $435$
• Weight: $2$
• Character orbit: 435.c
• Rep. character: $\chi_{435}(349,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	64	28	36
Cusp forms	56	28	28
Eisenstein series	8	0	8

Trace form

28 * q - 24 * q^4 - 4 * q^5 - 4 * q^6 - 28 * q^9 + 4 * q^10 + 16 * q^16 + 8 * q^19 + 8 * q^20 + 12 * q^24 - 12 * q^25 + 16 * q^26 - 16 * q^30 + 8 * q^31 + 24 * q^34 - 12 * q^35 + 24 * q^36 - 8 * q^39 - 56 * q^40 - 24 * q^41 + 8 * q^44 + 4 * q^45 + 56 * q^46 + 4 * q^49 - 24 * q^50 - 16 * q^51 + 4 * q^54 + 32 * q^55 - 24 * q^56 + 24 * q^59 - 20 * q^60 - 8 * q^61 - 24 * q^64 - 28 * q^65 + 32 * q^66 + 8 * q^69 - 20 * q^70 + 8 * q^71 - 64 * q^74 + 24 * q^76 + 32 * q^79 + 12 * q^80 + 28 * q^81 + 8 * q^84 - 8 * q^85 + 40 * q^86 + 24 * q^89 - 4 * q^90 - 64 * q^91 + 24 * q^94 - 8 * q^95 - 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.c.a	$435$	$2$	435.c	5.b	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}+(-i-2)q^{5}+\cdots\)
435.2.c.b	$435$	$2$	435.c	5.b	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓			435.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+(-2 i+1)q^{5}+\cdots\)
435.2.c.c	$435$	$2$	435.c	5.b	$2$	$4$	$4$	$3.473$	\(\Q(\zeta_{8})\)	None		✓			435.2.c.c	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+\beta_1 q^{3}+q^{4}+(2\beta_1-1)q^{5}+\cdots\)
435.2.c.d	$435$	$2$	435.c	5.b	$2$	$10$	$10$	$3.473$	10.0.\(\cdots\).1	None		✓			435.2.c.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}-\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
435.2.c.e	$435$	$2$	435.c	5.b	$2$	$10$	$10$	$3.473$	10.0.\(\cdots\).1	None		✓			435.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{6}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)

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

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