Space of modular forms of level 70, weight 3, and Character 70.l

• Label: 70.3.l
• Level: $70$
• Weight: $3$
• Character orbit: 70.l
• Rep. character: $\chi_{70}(23,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(70, [\chi])\).

	Total	New	Old
Modular forms	112	32	80
Cusp forms	80	32	48
Eisenstein series	32	0	32

Trace form

32 * q + 4 * q^5 - 16 * q^6 - 4 * q^7 - 16 * q^10 + 32 * q^11 - 72 * q^15 + 64 * q^16 + 92 * q^17 - 32 * q^18 - 24 * q^21 - 96 * q^22 + 72 * q^23 - 4 * q^25 - 32 * q^26 - 288 * q^27 - 64 * q^28 - 96 * q^30 - 248 * q^31 - 44 * q^33 + 232 * q^35 + 288 * q^36 - 28 * q^37 + 32 * q^38 + 112 * q^41 + 272 * q^42 + 280 * q^43 + 68 * q^45 + 72 * q^46 + 220 * q^47 - 192 * q^50 + 120 * q^51 + 204 * q^53 - 8 * q^55 - 112 * q^56 - 792 * q^57 + 160 * q^58 + 32 * q^60 - 528 * q^61 + 336 * q^62 - 256 * q^63 + 20 * q^65 - 80 * q^67 - 184 * q^68 + 144 * q^70 + 432 * q^71 - 64 * q^72 - 268 * q^73 + 464 * q^75 - 160 * q^76 + 676 * q^77 - 64 * q^78 - 16 * q^80 + 232 * q^81 + 128 * q^82 + 72 * q^83 - 128 * q^85 - 8 * q^86 + 388 * q^87 - 96 * q^88 - 1280 * q^90 - 864 * q^91 - 288 * q^92 - 132 * q^93 - 508 * q^95 - 32 * q^96 - 368 * q^97 - 224 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(70, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
70.3.l.a	$70$	$3$	70.l	35.l	$12$	$8$	$2$	$1.907$	8.0.3317760000.2	None		✓			70.3.l.a	$4$	$0$	\(4\)	\(-4\)	\(12\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\beta _{2}-\beta _{4})q^{2}+(-\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
70.3.l.b	$70$	$3$	70.l	35.l	$12$	$8$	$2$	$1.907$	8.0.303595776.1	None		✓			70.3.l.b	$4$	$0$	\(4\)	\(2\)	\(-6\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\beta _{3}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
70.3.l.c	$70$	$3$	70.l	35.l	$12$	$16$	$4$	$1.907$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		70.3.l.c	$4$	$0$	\(-8\)	\(2\)	\(-2\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\beta _{4}+\beta _{8})q^{2}+(-\beta _{3}-\beta _{10}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(70, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)