Space of modular forms of level 1824, weight 2, and Character 1824.q

• Label: 1824.2.q
• Level: $1824$
• Weight: $2$
• Character orbit: 1824.q
• Rep. character: $\chi_{1824}(577,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $18$
• Sturm bound: $640$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(640\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1824, [\chi])\).

	Total	New	Old
Modular forms	672	80	592
Cusp forms	608	80	528
Eisenstein series	64	0	64

Trace form

80 * q - 40 * q^9 - 8 * q^13 - 8 * q^21 - 40 * q^25 + 16 * q^37 + 16 * q^41 + 64 * q^49 + 16 * q^53 + 8 * q^57 + 8 * q^61 + 64 * q^65 - 8 * q^73 - 128 * q^77 - 40 * q^81 + 64 * q^85 + 32 * q^89 - 40 * q^93 + 32 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1824, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1824.2.q.a	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.a	$2$	$1$	\(0\)	\(-1\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{5}-q^{7}+\cdots\)
1824.2.q.b	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.b	$2$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+q^{7}+\cdots\)
1824.2.q.c	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.c	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+q^{7}+\cdots\)
1824.2.q.d	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.d	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3q^{7}-\zeta_{6}q^{9}-6q^{11}+\cdots\)
1824.2.q.e	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{5}+q^{7}+\cdots\)
1824.2.q.f	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.b	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-q^{7}+\cdots\)
1824.2.q.g	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.c	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-q^{7}+\cdots\)
1824.2.q.h	$1824$	$2$	1824.q	19.c	$3$	$2$	$1$	$14.565$	\(\Q(\sqrt{-3}) \)	None		✓			1824.2.q.d	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-3q^{7}-\zeta_{6}q^{9}+6q^{11}+\cdots\)
1824.2.q.i	$1824$	$2$	1824.q	19.c	$3$	$4$	$2$	$14.565$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1824.2.q.i	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
1824.2.q.j	$1824$	$2$	1824.q	19.c	$3$	$4$	$2$	$14.565$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1824.2.q.i	$2$	$0$	\(0\)	\(2\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+\cdots\)
1824.2.q.k	$1824$	$2$	1824.q	19.c	$3$	$6$	$3$	$14.565$	6.0.1714608.1	None		✓			1824.2.q.k	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{4})q^{3}+(-\beta _{3}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
1824.2.q.l	$1824$	$2$	1824.q	19.c	$3$	$6$	$3$	$14.565$	6.0.6967728.1	None		✓			1824.2.q.l	$2$	$0$	\(0\)	\(-3\)	\(4\)	\(-10\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{4})q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+\cdots\)
1824.2.q.m	$1824$	$2$	1824.q	19.c	$3$	$6$	$3$	$14.565$	6.0.591408.1	None		✓			1824.2.q.m	$2$	$0$	\(0\)	\(-3\)	\(6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{4})q^{3}+(2-2\beta _{4}+\beta _{5})q^{5}+\cdots\)
1824.2.q.n	$1824$	$2$	1824.q	19.c	$3$	$6$	$3$	$14.565$	6.0.1714608.1	None		✓			1824.2.q.k	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4})q^{3}+(-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1824.2.q.o	$1824$	$2$	1824.q	19.c	$3$	$6$	$3$	$14.565$	6.0.6967728.1	None		✓			1824.2.q.l	$2$	$0$	\(0\)	\(3\)	\(4\)	\(10\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots\)
1824.2.q.p	$1824$	$2$	1824.q	19.c	$3$	$6$	$3$	$14.565$	6.0.591408.1	None		✓			1824.2.q.m	$2$	$0$	\(0\)	\(3\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4})q^{3}+(2-2\beta _{4}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1824.2.q.q	$1824$	$2$	1824.q	19.c	$3$	$10$	$5$	$14.565$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			1824.2.q.q	$2$	$0$	\(0\)	\(-5\)	\(-2\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{5})q^{3}+(-\beta _{3}+\beta _{9})q^{5}+(1+\cdots)q^{7}+\cdots\)
1824.2.q.r	$1824$	$2$	1824.q	19.c	$3$	$10$	$5$	$14.565$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			1824.2.q.q	$2$	$0$	\(0\)	\(5\)	\(-2\)	\(-6\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{5})q^{3}+(-\beta _{3}+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1824, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1824, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)