Space of modular forms of level 3, weight 70, and trivial character

• Label: 3.70.a
• Level: $3$
• Weight: $70$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $23$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(23\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{70}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	24	12	12
Cusp forms	22	12	10
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	Dim
\(+\)	\(6\)
\(-\)	\(6\)

Trace form

\( 12 q + 18831599550 q^{2} + 3586833257181443225076 q^{4} + 1164829908436958237509656 q^{5} + 343055069760136649722795494 q^{6} - 117572717428940528567593369680 q^{7} + 53489353249344715486151627235240 q^{8} + 3337540673324322135087429314781132 q^{9} + O(q^{10}) \)

Decomposition of \(S_{70}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
3.70.a.a	$3$	$70$	3.a	1.a	$1$	$6$	$6$	$90.454$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-869363388\)	\(-10\!\cdots\!14\)	\(53\!\cdots\!20\)	\(-16\!\cdots\!16\)		$+$	$+$	$2^{51}\cdot 3^{33}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17\cdot 23^{2}$	$\mathrm{SU}(2)$	\(q+(-144893898+\beta _{1})q^{2}-3^{34}q^{3}+\cdots\)
3.70.a.b	$3$	$70$	3.a	1.a	$1$	$6$	$6$	$90.454$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(19700962938\)	\(10\!\cdots\!14\)	\(62\!\cdots\!36\)	\(47\!\cdots\!36\)		$-$	$-$	$2^{46}\cdot 3^{33}\cdot 5^{5}\cdot 7^{3}\cdot 11\cdot 17\cdot 23^{2}$	$\mathrm{SU}(2)$	\(q+(3283493823-\beta _{1})q^{2}+3^{34}q^{3}+\cdots\)

Decomposition of \(S_{70}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{70}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{70}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)