Space of modular forms of level 736, weight 2, and Character 736.h

• Label: 736.2.h
• Level: $736$
• Weight: $2$
• Character orbit: 736.h
• Rep. character: $\chi_{736}(367,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(736, [\chi])\).

	Total	New	Old
Modular forms	104	26	78
Cusp forms	88	22	66
Eisenstein series	16	4	12

Trace form

\( 22 q + 4 q^{3} + 14 q^{9} + 10 q^{25} + 4 q^{27} + 24 q^{35} - 4 q^{41} + 6 q^{49} + 16 q^{59} - 4 q^{73} + 36 q^{75} - 26 q^{81}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(736, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
736.2.h.a	$736$	$2$	736.h	184.h	$2$	$4$	$4$	$5.877$	\(\Q(i, \sqrt{14})\)	None					184.2.h.a	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+\beta _{3}q^{5}+q^{9}+\beta _{2}q^{11}-4\beta _{1}q^{13}+\cdots\)
736.2.h.b	$736$	$2$	736.h	184.h	$2$	$6$	$6$	$5.877$	6.0.8869743.1	\(\Q(\sqrt{-23}) \)					184.2.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+(3+\beta _{2}-\beta _{5})q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
736.2.h.c	$736$	$2$	736.h	184.h	$2$	$12$	$12$	$5.877$	12.0.\(\cdots\).2	None			✓		184.2.h.c	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{10}\cdot 23$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}-\beta _{8}q^{5}-\beta _{4}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(736, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 3}\)