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

• Label: 1872.2.n
• Level: $1872$
• Weight: $2$
• Character orbit: 1872.n
• Rep. character: $\chi_{1872}(1871,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $5$
• Sturm bound: $672$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(7\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	360	28	332
Cusp forms	312	28	284
Eisenstein series	48	0	48

Trace form

\( 28 q + O(q^{10}) \)

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.n.a	$1872$	$2$	1872.n	156.h	$2$	$4$	$4$	$14.948$	\(\Q(\sqrt{-2}, \sqrt{13})\)	\(\Q(\sqrt{-13}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta _{2})q^{7}-\beta _{3}q^{11}+\beta _{2}q^{13}+\cdots\)
1872.2.n.b	$1872$	$2$	1872.n	156.h	$2$	$4$	$4$	$14.948$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{3}q^{5}+(2+\zeta_{8})q^{13}+5\zeta_{8}^{2}q^{17}+\cdots\)
1872.2.n.c	$1872$	$2$	1872.n	156.h	$2$	$4$	$4$	$14.948$	\(\Q(\sqrt{-2}, \sqrt{13})\)	\(\Q(\sqrt{-13}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta _{2})q^{7}-\beta _{3}q^{11}+\beta _{2}q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
1872.2.n.d	$1872$	$2$	1872.n	156.h	$2$	$8$	$8$	$14.948$	8.0.764411904.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{1}q^{7}-\beta _{4}q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots\)
1872.2.n.e	$1872$	$2$	1872.n	156.h	$2$	$8$	$8$	$14.948$	8.0.764411904.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{1}q^{7}+\beta _{4}q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \)