Space of modular forms of level 16, weight 44, and trivial character

• Label: 16.44.a
• Level: $16$
• Weight: $44$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $6$
• Sturm bound: $88$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(88\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_0(16))\).

	Total	New	Old
Modular forms	89	22	67
Cusp forms	83	21	62
Eisenstein series	6	1	5

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
\(+\)	\(11\)
\(-\)	\(10\)

Trace form

\( 21 q + 10460353204 q^{3} - 247839723078602 q^{5} + 574012688698122568 q^{7} + 2294703116712725897017 q^{9} + O(q^{10}) \)

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_0(16))\) 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
16.44.a.a	$16$	$44$	16.a	1.a	$1$	$2$	$2$	$187.377$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(12981630984\)	\(-39\!\cdots\!00\)	\(-11\!\cdots\!08\)		$-$	$-$	$2^{8}\cdot 3\cdot 5\cdot 11$	$\mathrm{SU}(2)$	\(q+(6490815492-\beta )q^{3}+(-199331355641250+\cdots)q^{5}+\cdots\)
16.44.a.b	$16$	$44$	16.a	1.a	$1$	$2$	$2$	$187.377$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(22341634056\)	\(-47\!\cdots\!20\)	\(22\!\cdots\!28\)		$-$	$-$	$2^{8}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(11170817028-\beta )q^{3}+(-23660329199010+\cdots)q^{5}+\cdots\)
16.44.a.c	$16$	$44$	16.a	1.a	$1$	$3$	$3$	$187.377$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-24401437812\)	\(53\!\cdots\!70\)	\(-30\!\cdots\!56\)		$-$	$-$	$2^{25}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(-8133812604+\beta _{1})q^{3}+(178401793591390+\cdots)q^{5}+\cdots\)
16.44.a.d	$16$	$44$	16.a	1.a	$1$	$3$	$3$	$187.377$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7902569844\)	\(29\!\cdots\!30\)	\(25\!\cdots\!36\)		$-$	$-$	$2^{24}\cdot 3^{6}\cdot 5\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+(-2634189948+\beta _{1})q^{3}+(9956588758110+\cdots)q^{5}+\cdots\)
16.44.a.e	$16$	$44$	16.a	1.a	$1$	$5$	$5$	$187.377$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-8106631116\)	\(-35\!\cdots\!50\)	\(21\!\cdots\!68\)		$+$	$+$	$2^{72}\cdot 3^{9}\cdot 5^{3}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+(-1621326223+\beta _{1})q^{3}+(-70805587198428+\cdots)q^{5}+\cdots\)
16.44.a.f	$16$	$44$	16.a	1.a	$1$	$6$	$6$	$187.377$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(15547726936\)	\(-12\!\cdots\!32\)	\(-34\!\cdots\!00\)		$+$	$+$	$2^{109}\cdot 3^{11}\cdot 5^{3}\cdot 7^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(2591287823-\beta _{1})q^{3}+(-2150594076331+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{44}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{44}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{44}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)