Space of modular forms of level 1072, weight 2, and Character 1072.g

• Label: 1072.2.g
• Level: $1072$
• Weight: $2$
• Character orbit: 1072.g
• Rep. character: $\chi_{1072}(1071,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $5$
• Sturm bound: $272$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1072 = 2^{4} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1072.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 268 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(272\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1072, [\chi])\).

	Total	New	Old
Modular forms	142	34	108
Cusp forms	130	34	96
Eisenstein series	12	0	12

Trace form

\( 34 q + 22 q^{9} + 12 q^{17} - 16 q^{21} - 34 q^{25} - 24 q^{29} - 8 q^{37} + 42 q^{49} + 44 q^{73} + 24 q^{77} - 14 q^{81} - 12 q^{89} - 32 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1072, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1072.2.g.a	$1072$	$2$	1072.g	268.d	$2$	$2$	$2$	$8.560$	\(\Q(\sqrt{-67}) \)	\(\Q(\sqrt{-67}) \)		✓			1072.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{9}-q^{17}-\beta q^{19}-\beta q^{23}+5q^{25}+\cdots\)
1072.2.g.b	$1072$	$2$	1072.g	268.d	$2$	$4$	$4$	$8.560$	\(\Q(i, \sqrt{13})\)	None		✓			1072.2.g.b	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-10\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-2-\beta _{3})q^{7}+\cdots\)
1072.2.g.c	$1072$	$2$	1072.g	268.d	$2$	$4$	$4$	$8.560$	\(\Q(\sqrt{-3}, \sqrt{-67})\)	\(\Q(\sqrt{-67}) \)		✓			1072.2.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{9}+(1-\beta _{2})q^{17}+(-2\beta _{1}-\beta _{3})q^{19}+\cdots\)
1072.2.g.d	$1072$	$2$	1072.g	268.d	$2$	$4$	$4$	$8.560$	\(\Q(i, \sqrt{13})\)	None		✓			1072.2.g.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(10\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}-\beta _{2}q^{5}+(2+\beta _{3})q^{7}+\cdots\)
1072.2.g.e	$1072$	$2$	1072.g	268.d	$2$	$20$	$20$	$8.560$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		1072.2.g.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{8}q^{5}-\beta _{13}q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1072, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1072, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 3}\)