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

• Label: 1872.2.by
• Level: $1872$
• Weight: $2$
• Character orbit: 1872.by
• Rep. character: $\chi_{1872}(433,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $15$
• Sturm bound: $672$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.by (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(672\)
Trace bound:			\(17\)
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	72	648
Cusp forms	624	68	556
Eisenstein series	96	4	92

Trace form

\( 68 q - 3 q^{7} + O(q^{10}) \)

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.by.a	$1872$	$2$	1872.by	13.e	$6$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-6+3\zeta_{6})q^{7}+(-4+3\zeta_{6})q^{13}+\cdots\)
1872.2.by.b	$1872$	$2$	1872.by	13.e	$6$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+(2+\cdots)q^{11}+\cdots\)
1872.2.by.c	$1872$	$2$	1872.by	13.e	$6$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+\zeta_{6})q^{7}+(4-\zeta_{6})q^{13}+(-4+\cdots)q^{19}+\cdots\)
1872.2.by.d	$1872$	$2$	1872.by	13.e	$6$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{5}+(-1-3\zeta_{6})q^{13}+\cdots\)
1872.2.by.e	$1872$	$2$	1872.by	13.e	$6$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+(-3+\cdots)q^{13}+\cdots\)
1872.2.by.f	$1872$	$2$	1872.by	13.e	$6$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-4\zeta_{6})q^{5}+(2-\zeta_{6})q^{7}+(-2-2\zeta_{6})q^{11}+\cdots\)
1872.2.by.g	$1872$	$2$	1872.by	13.e	$6$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{12}^{2})q^{5}+(-2-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1872.2.by.h	$1872$	$2$	1872.by	13.e	$6$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1872.2.by.i	$1872$	$2$	1872.by	13.e	$6$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{3}q^{5}+(-4+3\zeta_{12}^{2})q^{13}+(-\zeta_{12}+\cdots)q^{17}+\cdots\)
1872.2.by.j	$1872$	$2$	1872.by	13.e	$6$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{-43})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
1872.2.by.k	$1872$	$2$	1872.by	13.e	$6$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{12}^{2})q^{5}+(1+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1872.2.by.l	$1872$	$2$	1872.by	13.e	$6$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{5}+(2+2\beta _{2})q^{7}+(2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
1872.2.by.m	$1872$	$2$	1872.by	13.e	$6$	$8$	$4$	$14.948$	8.0.649638144.4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{6})q^{5}+(-1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1872.2.by.n	$1872$	$2$	1872.by	13.e	$6$	$8$	$4$	$14.948$	8.0.195105024.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3}-\beta _{5}+\beta _{6})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1872.2.by.o	$1872$	$2$	1872.by	13.e	$6$	$16$	$8$	$14.948$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{16}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{12}q^{5}-\beta _{2}q^{7}+(-\beta _{5}+\beta _{8}-\beta _{12}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)