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

• Label: 1824.2.p
• Level: $1824$
• Weight: $2$
• Character orbit: 1824.p
• Rep. character: $\chi_{1824}(113,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $2$
• Sturm bound: $640$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(640\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	336	84	252
Cusp forms	304	76	228
Eisenstein series	32	8	24

Trace form

\( 76 q + 8 q^{7} - 4 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1824.2.p.a	$1824$	$2$	1824.p	456.p	$2$	$12$	$12$	$14.565$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	\(\Q(\sqrt{-38}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{8}q^{3}+(\beta _{9}-\beta _{10})q^{7}+\beta _{10}q^{9}+\cdots\)
1824.2.p.b	$1824$	$2$	1824.p	456.p	$2$	$64$	$64$	$14.565$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1824, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)