Space of modular forms of level 720, weight 2, and Character 720.bm

• Label: 720.2.bm
• Level: $720$
• Weight: $2$
• Character orbit: 720.bm
• Rep. character: $\chi_{720}(109,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $116$
• Newform subspaces: $8$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(720, [\chi])\).

	Total	New	Old
Modular forms	304	124	180
Cusp forms	272	116	156
Eisenstein series	32	8	24

Trace form

116 * q - 4 * q^4 + 2 * q^5 - 8 * q^10 + 4 * q^11 + 20 * q^14 - 8 * q^16 + 4 * q^19 + 16 * q^20 + 8 * q^26 + 4 * q^29 + 16 * q^31 - 24 * q^34 - 48 * q^40 + 24 * q^44 - 4 * q^46 + 84 * q^49 - 4 * q^50 + 8 * q^56 + 20 * q^59 + 12 * q^61 - 64 * q^64 - 4 * q^65 - 52 * q^70 - 16 * q^74 - 40 * q^76 + 16 * q^79 - 64 * q^80 + 8 * q^85 + 36 * q^86 - 16 * q^91 - 84 * q^94 + 28 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(720, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
720.2.bm.a	$720$	$2$	720.bm	80.q	$4$	$2$	$1$	$5.749$	\(\Q(\sqrt{-1}) \)	None					80.2.q.a	$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+2 i q^{4}+(-i-2)q^{5}+\cdots\)
720.2.bm.b	$720$	$2$	720.bm	80.q	$4$	$2$	$1$	$5.749$	\(\Q(\sqrt{-1}) \)	None					80.2.q.a	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{2}+2 i q^{4}+(-2 i-1)q^{5}+\cdots\)
720.2.bm.c	$720$	$2$	720.bm	80.q	$4$	$4$	$2$	$5.749$	\(\Q(\zeta_{8})\)	None		✓			720.2.bm.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
720.2.bm.d	$720$	$2$	720.bm	80.q	$4$	$4$	$2$	$5.749$	\(\Q(\zeta_{8})\)	None		✓			720.2.bm.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
720.2.bm.e	$720$	$2$	720.bm	80.q	$4$	$8$	$4$	$5.749$	8.0.3317760000.5	\(\Q(\sqrt{-15}) \)		✓			720.2.bm.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{4}-\beta _{6})q^{5}+(2\beta _{4}+\cdots)q^{8}+\cdots\)
720.2.bm.f	$720$	$2$	720.bm	80.q	$4$	$16$	$8$	$5.749$	16.0.\(\cdots\).1	None					80.2.q.c	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{2}+(-1+\beta _{4}-\beta _{7}+\beta _{8})q^{4}+\cdots\)
720.2.bm.g	$720$	$2$	720.bm	80.q	$4$	$32$	$16$	$5.749$		None		✓			720.2.bm.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
720.2.bm.h	$720$	$2$	720.bm	80.q	$4$	$48$	$24$	$5.749$		None			✓		240.2.bl.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(720, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)