Space of modular forms of level 1872, weight 2, and Character 1872.dv

• Label: 1872.2.dv
• Level: $1872$
• Weight: $2$
• Character orbit: 1872.dv
• Rep. character: $\chi_{1872}(719,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $5$
• Sturm bound: $672$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.dv (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

	Total	New	Old
Modular forms	720	56	664
Cusp forms	624	56	568
Eisenstein series	96	0	96

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1872.2.dv.a	$1872$	$2$	1872.dv	156.r	$6$	$4$	$2$	$14.948$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\beta _{1}+\beta _{3})q^{5}+(-3+3\beta _{2})q^{7}+\cdots\)
1872.2.dv.b	$1872$	$2$	1872.dv	156.r	$6$	$4$	$2$	$14.948$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\beta _{1}+\beta _{3})q^{5}+(3-3\beta _{2})q^{7}+(3\beta _{1}+\cdots)q^{11}+\cdots\)
1872.2.dv.c	$1872$	$2$	1872.dv	156.r	$6$	$8$	$4$	$14.948$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{5}+(-2-\zeta_{24}+2\zeta_{24}^{2}+\cdots)q^{13}+\cdots\)
1872.2.dv.d	$1872$	$2$	1872.dv	156.r	$6$	$20$	$10$	$14.948$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{5}+(\beta _{7}-\beta _{12})q^{7}+(-\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots\)
1872.2.dv.e	$1872$	$2$	1872.dv	156.r	$6$	$20$	$10$	$14.948$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{5}+(-\beta _{7}+\beta _{12})q^{7}+(\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)