Space of modular forms of level 70, weight 4, and Character 70.c

• Label: 70.4.c
• Level: $70$
• Weight: $4$
• Character orbit: 70.c
• Rep. character: $\chi_{70}(29,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(70, [\chi])\).

	Total	New	Old
Modular forms	40	8	32
Cusp forms	32	8	24
Eisenstein series	8	0	8

Trace form

8 * q - 32 * q^4 + 4 * q^5 - 196 * q^9 - 56 * q^10 - 36 * q^11 + 56 * q^14 + 40 * q^15 + 128 * q^16 - 96 * q^19 - 16 * q^20 - 196 * q^21 + 636 * q^25 + 368 * q^26 + 316 * q^29 - 200 * q^30 + 72 * q^31 - 784 * q^34 + 56 * q^35 + 784 * q^36 - 884 * q^39 + 224 * q^40 + 400 * q^41 + 144 * q^44 + 1548 * q^45 - 80 * q^46 - 392 * q^49 + 456 * q^50 - 812 * q^51 - 2016 * q^54 + 896 * q^55 - 224 * q^56 - 1176 * q^59 - 160 * q^60 - 1176 * q^61 - 512 * q^64 + 1096 * q^65 + 416 * q^66 - 5480 * q^69 - 504 * q^70 + 2360 * q^71 + 1808 * q^74 - 3360 * q^75 + 384 * q^76 + 404 * q^79 + 64 * q^80 + 3136 * q^81 + 784 * q^84 - 492 * q^85 - 2368 * q^86 + 2536 * q^89 + 3048 * q^90 + 140 * q^91 + 832 * q^94 + 2260 * q^95 + 8184 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(70, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
70.4.c.a	$70$	$4$	70.c	5.b	$2$	$2$	$2$	$4.130$	\(\Q(\sqrt{-1}) \)	None		✓			70.4.c.a	$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+7 i q^{3}-4 q^{4}+(5 i+10)q^{5}+\cdots\)
70.4.c.b	$70$	$4$	70.c	5.b	$2$	$6$	$6$	$4.130$	6.0.\(\cdots\).1	None		✓	✓		70.4.c.b	$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{3}q^{2}+(-2\beta _{3}+\beta _{5})q^{3}-4q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(70, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)