Space of modular forms of level 2380, weight 2, and Character 2380.q

• Label: 2380.2.q
• Level: $2380$
• Weight: $2$
• Character orbit: 2380.q
• Rep. character: $\chi_{2380}(681,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $88$
• Newform subspaces: $8$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2380.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(864\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2380, [\chi])\).

	Total	New	Old
Modular forms	888	88	800
Cusp forms	840	88	752
Eisenstein series	48	0	48

Trace form

88 * q - 4 * q^3 - 4 * q^5 - 12 * q^7 - 44 * q^9 + 4 * q^11 - 8 * q^17 + 16 * q^19 + 4 * q^21 - 44 * q^25 + 32 * q^27 - 8 * q^29 + 12 * q^31 + 8 * q^33 - 4 * q^35 + 16 * q^37 + 20 * q^39 - 16 * q^41 - 56 * q^43 - 8 * q^45 - 4 * q^47 - 12 * q^49 + 4 * q^53 - 20 * q^59 - 12 * q^61 - 16 * q^63 + 4 * q^65 - 88 * q^69 - 40 * q^71 + 8 * q^73 - 4 * q^75 + 36 * q^77 + 16 * q^79 - 36 * q^81 - 80 * q^83 + 12 * q^87 + 8 * q^89 + 12 * q^93 + 88 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2380, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2380.2.q.a	$2380$	$2$	2380.q	7.c	$3$	$2$	$1$	$19.004$	\(\Q(\sqrt{-3}) \)	None		✓			2380.2.q.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
2380.2.q.b	$2380$	$2$	2380.q	7.c	$3$	$2$	$1$	$19.004$	\(\Q(\sqrt{-3}) \)	None		✓			2380.2.q.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
2380.2.q.c	$2380$	$2$	2380.q	7.c	$3$	$4$	$2$	$19.004$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		✓			2380.2.q.c	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(-10\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{3}-\beta _{1}q^{5}+(-3-\beta _{1})q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
2380.2.q.d	$2380$	$2$	2380.q	7.c	$3$	$4$	$2$	$19.004$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		✓			2380.2.q.d	$2$	$0$	\(0\)	\(1\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-1-3\beta _{3})q^{7}+\cdots\)
2380.2.q.e	$2380$	$2$	2380.q	7.c	$3$	$6$	$3$	$19.004$	6.0.2101707.2	None		✓			2380.2.q.e	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{5}+(1-3\beta _{3}+\cdots)q^{7}+\cdots\)
2380.2.q.f	$2380$	$2$	2380.q	7.c	$3$	$18$	$9$	$19.004$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			2380.2.q.f	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{4})q^{3}-\beta _{5}q^{5}-\beta _{6}q^{7}+\cdots\)
2380.2.q.g	$2380$	$2$	2380.q	7.c	$3$	$24$	$12$	$19.004$		None		✓			2380.2.q.g	$2$	$0$	\(0\)	\(-1\)	\(12\)	\(-4\)		$\mathrm{SU}(2)[C_{3}]$
2380.2.q.h	$2380$	$2$	2380.q	7.c	$3$	$28$	$14$	$19.004$		None		✓	✓		2380.2.q.h	$2$	$0$	\(0\)	\(-1\)	\(-14\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2380, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(595, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1190, [\chi])\)\(^{\oplus 2}\)