Space of modular forms of level 726, weight 2, and Character 726.b

• Label: 726.2.b
• Level: $726$
• Weight: $2$
• Character orbit: 726.b
• Rep. character: $\chi_{726}(725,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $6$
• Sturm bound: $264$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(264\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(726, [\chi])\).

	Total	New	Old
Modular forms	156	36	120
Cusp forms	108	36	72
Eisenstein series	48	0	48

Trace form

36 * q + 6 * q^3 + 36 * q^4 + 2 * q^9 + 6 * q^12 + 8 * q^15 + 36 * q^16 - 64 * q^25 - 18 * q^27 + 28 * q^31 - 4 * q^34 + 2 * q^36 - 24 * q^42 - 16 * q^45 + 6 * q^48 + 28 * q^58 + 8 * q^60 + 36 * q^64 + 20 * q^67 + 16 * q^69 - 32 * q^70 + 6 * q^75 + 32 * q^78 + 26 * q^81 - 28 * q^82 + 8 * q^91 - 12 * q^93 - 120 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(726, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
726.2.b.a	$726$	$2$	726.b	33.d	$2$	$2$	$2$	$5.797$	\(\Q(\sqrt{-2}) \)	None		✓			726.2.b.a	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
726.2.b.b	$726$	$2$	726.b	33.d	$2$	$2$	$2$	$5.797$	\(\Q(\sqrt{-2}) \)	None		✓			726.2.b.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
726.2.b.c	$726$	$2$	726.b	33.d	$2$	$8$	$8$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(-8\)	\(-3\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
726.2.b.d	$726$	$2$	726.b	33.d	$2$	$8$	$8$	$5.797$	8.0.3588489216.5	None		✓			726.2.b.d	$2$	$0$	\(-8\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(\beta _{1}+\beta _{6})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
726.2.b.e	$726$	$2$	726.b	33.d	$2$	$8$	$8$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(8\)	\(-3\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
726.2.b.f	$726$	$2$	726.b	33.d	$2$	$8$	$8$	$5.797$	8.0.3588489216.5	None		✓			726.2.b.d	$2$	$0$	\(8\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{1}+\beta _{6})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(726, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(726, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)