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

• Label: 726.2.h
• Level: $726$
• Weight: $2$
• Character orbit: 726.h
• Rep. character: $\chi_{726}(161,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $144$
• Newform subspaces: $12$
• Sturm bound: $264$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(264\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	624	144	480
Cusp forms	432	144	288
Eisenstein series	192	0	192

Trace form

144 * q - 6 * q^3 - 36 * q^4 + 5 * q^6 + 18 * q^9 + 14 * q^12 + 12 * q^15 - 36 * q^16 + 5 * q^18 + 30 * q^19 - 5 * q^24 + 64 * q^25 - 12 * q^27 - 10 * q^28 - 30 * q^30 - 38 * q^31 - 36 * q^34 - 7 * q^36 - 20 * q^37 - 10 * q^39 - 10 * q^40 + 4 * q^42 + 16 * q^45 + 20 * q^46 - 6 * q^48 + 80 * q^49 + 15 * q^51 + 20 * q^52 - 35 * q^57 + 42 * q^58 - 8 * q^60 + 20 * q^61 - 10 * q^63 - 36 * q^64 + 20 * q^67 - 6 * q^69 + 42 * q^70 + 20 * q^72 - 10 * q^73 + 39 * q^75 + 48 * q^78 - 20 * q^79 + 14 * q^81 - 2 * q^82 - 60 * q^85 - 10 * q^90 - 128 * q^91 + 22 * q^93 - 80 * q^94 + 70 * 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.h.a	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(-2\)	\(-3\)	\(5\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\beta _{2}+\beta _{4}-\beta _{6})q^{2}+\beta _{5}q^{3}+\cdots\)
726.2.h.b	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.64000000.1	None		✓			726.2.b.a	$8$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{6}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
726.2.h.c	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(-2\)	\(2\)	\(-5\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{3}+\beta _{4})q^{3}+\beta _{6}q^{4}+\cdots\)
726.2.h.d	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{6}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
726.2.h.e	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.64000000.1	None					66.2.b.a	$8$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{6}q^{2}+(1-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
726.2.h.f	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(2\)	\(-3\)	\(5\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(1-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+\cdots\)
726.2.h.g	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.64000000.1	None		✓			726.2.b.a	$8$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
726.2.h.h	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(2\)	\(2\)	\(-5\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(1-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+(1+\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
726.2.h.i	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.64000000.1	None					66.2.b.a	$8$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
726.2.h.j	$726$	$2$	726.h	33.f	$10$	$8$	$2$	$5.797$	8.0.185640625.1	None					66.2.h.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
726.2.h.k	$726$	$2$	726.h	33.f	$10$	$32$	$8$	$5.797$		None		✓			726.2.b.d	$8$	$0$	\(-8\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
726.2.h.l	$726$	$2$	726.h	33.f	$10$	$32$	$8$	$5.797$		None		✓			726.2.b.d	$8$	$0$	\(8\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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