Space of modular forms of level 2, weight 70, and trivial character

• Label: 2.70.a
• Level: $2$
• Weight: $70$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $17$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(17\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{70}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	18	6	12
Cusp forms	16	6	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.

\(2\)	Dim
\(+\)	\(3\)
\(-\)	\(3\)

Trace form

\( 6 q - 8116452590112840 q^{3} + 1770887431076116955136 q^{4} + 1426588595791134963780420 q^{5} - 671420440364298705385291776 q^{6} - 116335089770189171139669400080 q^{7} + 3672920218335960101345358967935918 q^{9} + O(q^{10}) \)

Decomposition of \(S_{70}^{\mathrm{new}}(\Gamma_0(2))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
2.70.a.a	$2$	$70$	2.a	1.a	$1$	$3$	$3$	$60.303$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-51539607552\)	\(15\!\cdots\!12\)	\(20\!\cdots\!70\)	\(-20\!\cdots\!96\)		$+$	$+$	$2^{24}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 11\cdot 17\cdot 23$	$\mathrm{SU}(2)$	\(q-2^{34}q^{2}+(5160893455497204+\cdots)q^{3}+\cdots\)
2.70.a.b	$2$	$70$	2.a	1.a	$1$	$3$	$3$	$60.303$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(51539607552\)	\(-23\!\cdots\!52\)	\(-58\!\cdots\!50\)	\(92\!\cdots\!16\)		$-$	$-$	$2^{24}\cdot 3^{5}\cdot 5^{4}\cdot 7\cdot 23$	$\mathrm{SU}(2)$	\(q+2^{34}q^{2}+(-7866377652201484+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{70}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

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