Space of modular forms of level 1860, weight 2, and Character 1860.q

• Label: 1860.2.q
• Level: $1860$
• Weight: $2$
• Character orbit: 1860.q
• Rep. character: $\chi_{1860}(1141,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $44$
• Newform subspaces: $9$
• Sturm bound: $768$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(768\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1860, [\chi])\).

	Total	New	Old
Modular forms	792	44	748
Cusp forms	744	44	700
Eisenstein series	48	0	48

Trace form

44 * q - 2 * q^3 - 4 * q^7 - 22 * q^9 - 4 * q^11 + 2 * q^13 - 20 * q^17 + 2 * q^19 - 4 * q^21 + 16 * q^23 - 22 * q^25 + 4 * q^27 - 32 * q^29 + 4 * q^31 - 16 * q^33 - 16 * q^35 - 14 * q^37 + 20 * q^39 - 24 * q^41 - 18 * q^43 + 16 * q^47 - 14 * q^49 + 4 * q^51 + 12 * q^53 + 4 * q^55 + 2 * q^57 - 12 * q^59 + 32 * q^61 + 8 * q^63 - 8 * q^67 + 4 * q^71 + 10 * q^73 - 2 * q^75 - 16 * q^77 + 4 * q^79 - 22 * q^81 - 20 * q^83 + 24 * q^85 - 4 * q^87 + 32 * q^89 - 56 * q^91 - 10 * q^93 - 28 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1860, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1860.2.q.a	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	\(\Q(\sqrt{-3}) \)	None		✓			1860.2.q.a	$2$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots\)
1860.2.q.b	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	\(\Q(\sqrt{-3}) \)	None		✓			1860.2.q.b	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+4\zeta_{6}q^{11}+\cdots\)
1860.2.q.c	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	\(\Q(\sqrt{-3}) \)	None		✓			1860.2.q.c	$2$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
1860.2.q.d	$1860$	$2$	1860.q	31.c	$3$	$2$	$1$	$14.852$	\(\Q(\sqrt{-3}) \)	None		✓			1860.2.q.d	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
1860.2.q.e	$1860$	$2$	1860.q	31.c	$3$	$4$	$2$	$14.852$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			1860.2.q.e	$2$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}-\beta _{1}q^{9}+(3\beta _{1}+\cdots)q^{11}+\cdots\)
1860.2.q.f	$1860$	$2$	1860.q	31.c	$3$	$6$	$3$	$14.852$	6.0.2958147.4	None		✓			1860.2.q.f	$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1860.2.q.g	$1860$	$2$	1860.q	31.c	$3$	$6$	$3$	$14.852$	6.0.64616643.2	None		✓			1860.2.q.g	$2$	$0$	\(0\)	\(3\)	\(3\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1})q^{3}-\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1860.2.q.h	$1860$	$2$	1860.q	31.c	$3$	$8$	$4$	$14.852$	8.0.\(\cdots\).2	None		✓			1860.2.q.h	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{3}+(-1+\beta _{4})q^{5}+(-\beta _{1}+2\beta _{4}+\cdots)q^{7}+\cdots\)
1860.2.q.i	$1860$	$2$	1860.q	31.c	$3$	$12$	$6$	$14.852$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		1860.2.q.i	$2$	$0$	\(0\)	\(-6\)	\(6\)	\(-2\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{3}+(1-\beta _{7})q^{5}+(-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1860, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1860, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(372, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)