Space of modular forms of level 2, weight 72, and trivial character

• Label: 2.72.a
• Level: $2$
• Weight: $72$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	19	5	14
Cusp forms	17	5	12
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
\(+\)	\(3\)
\(-\)	\(2\)

Trace form

\( 5 q - 34359738368 q^{2} - 70927982282139588 q^{3} + 5902958103587056517120 q^{4} + 8770870597804349527314150 q^{5} - 2599421508451315417696174080 q^{6} - 977029489621691011470940739624 q^{7} - 40564819207303340847894502572032 q^{8} - 10628802685401817991279833906512615 q^{9} + O(q^{10}) \)

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_0(2))\) 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
2.72.a.a	$2$	$72$	2.a	1.a	$1$	$2$	$2$	$63.849$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(68719476736\)	\(-73\!\cdots\!24\)	\(40\!\cdots\!00\)	\(-29\!\cdots\!52\)		$-$	$-$	$2^{7}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+2^{35}q^{2}+(-36645276287423412+\cdots)q^{3}+\cdots\)
2.72.a.b	$2$	$72$	2.a	1.a	$1$	$3$	$3$	$63.849$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-103079215104\)	\(23\!\cdots\!36\)	\(47\!\cdots\!50\)	\(-68\!\cdots\!72\)		$+$	$+$	$2^{22}\cdot 3^{6}\cdot 5^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q-2^{35}q^{2}+(787523430902412+\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{72}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{72}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{72}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)