Space of modular forms of level 35, weight 5, and Character 35.d

• Label: 35.5.d
• Level: $35$
• Weight: $5$
• Character orbit: 35.d
• Rep. character: $\chi_{35}(6,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(35, [\chi])\).

	Total	New	Old
Modular forms	18	12	6
Cusp forms	14	12	2
Eisenstein series	4	0	4

Trace form

12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9 + 126 * q^11 + 78 * q^14 + 50 * q^15 + 578 * q^16 + 734 * q^18 - 642 * q^21 + 2264 * q^22 - 756 * q^23 - 1500 * q^25 + 1414 * q^28 - 2190 * q^29 + 1600 * q^30 - 8682 * q^32 - 150 * q^35 - 3582 * q^36 + 5564 * q^37 + 8634 * q^39 + 5580 * q^42 + 3944 * q^43 - 11196 * q^44 + 7844 * q^46 - 8796 * q^49 + 750 * q^50 + 7206 * q^51 + 11760 * q^53 - 6606 * q^56 - 12900 * q^57 - 18496 * q^58 - 11700 * q^60 - 4310 * q^63 + 20146 * q^64 - 750 * q^65 - 24096 * q^67 + 14400 * q^70 - 5664 * q^71 + 39214 * q^72 + 17604 * q^74 + 26904 * q^77 + 20100 * q^78 - 1590 * q^79 - 11912 * q^81 - 43128 * q^84 + 1050 * q^85 + 17604 * q^86 - 7268 * q^88 - 7182 * q^91 - 60252 * q^92 - 70980 * q^93 - 3000 * q^95 + 57714 * q^98 + 23084 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.5.d.a	$35$	$5$	35.d	7.b	$2$	$12$	$12$	$3.618$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	35.5.d.a	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(-50\)	$2^{3}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(35, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)