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

• Label: 1824.2.j
• Level: $1824$
• Weight: $2$
• Character orbit: 1824.j
• Rep. character: $\chi_{1824}(1103,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $640$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(640\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	336	72	264
Cusp forms	304	72	232
Eisenstein series	32	0	32

Trace form

\( 72 q + O(q^{10}) \)

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.j.a	$1824$	$2$	1824.j	24.f	$2$	$4$	$4$	$14.565$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					456.2.j.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{3}-\beta _{3}q^{7}+(-1+2\beta _{1}+\cdots)q^{9}+\cdots\)
1824.2.j.b	$1824$	$2$	1824.j	24.f	$2$	$8$	$8$	$14.565$	8.0.170772624.1	None					456.2.j.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{6}q^{7}+(1+\beta _{1}+\beta _{7})q^{9}+\cdots\)
1824.2.j.c	$1824$	$2$	1824.j	24.f	$2$	$12$	$12$	$14.565$	12.0.\(\cdots\).1	None					456.2.j.c	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(\beta _{1}+\beta _{4})q^{5}+\beta _{9}q^{7}+(1+\cdots)q^{9}+\cdots\)
1824.2.j.d	$1824$	$2$	1824.j	24.f	$2$	$24$	$24$	$14.565$		None					456.2.j.e	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1824.2.j.e	$1824$	$2$	1824.j	24.f	$2$	$24$	$24$	$14.565$		None					456.2.j.d	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1824, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)