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

• Label: 1872.2.t
• Level: $1872$
• Weight: $2$
• Character orbit: 1872.t
• Rep. character: $\chi_{1872}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $68$
• Newform subspaces: $22$
• Sturm bound: $672$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.t (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

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

\( 68 q + 2 q^{5} + 3 q^{7} + O(q^{10}) \)

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.t.a	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3q^{5}-4\zeta_{6}q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
1872.2.t.b	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3q^{5}+(3+\zeta_{6})q^{13}-\zeta_{6}q^{17}+(-4+\cdots)q^{23}+\cdots\)
1872.2.t.c	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3q^{5}+2\zeta_{6}q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1872.2.t.d	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{5}-\zeta_{6}q^{7}+(-1+\zeta_{6})q^{11}+(1+\cdots)q^{13}+\cdots\)
1872.2.t.e	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{5}+\zeta_{6}q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1872.2.t.f	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{5}+\zeta_{6}q^{7}+(5-5\zeta_{6})q^{11}+(-3+\cdots)q^{13}+\cdots\)
1872.2.t.g	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q-\zeta_{6}q^{7}+(4-3\zeta_{6})q^{13}+8\zeta_{6}q^{19}+\cdots\)
1872.2.t.h	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+5\zeta_{6}q^{7}+(-4+\zeta_{6})q^{13}+8\zeta_{6}q^{19}+\cdots\)
1872.2.t.i	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}-2\zeta_{6}q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1872.2.t.j	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}+2\zeta_{6}q^{7}+(2-2\zeta_{6})q^{11}+(-3+\cdots)q^{13}+\cdots\)
1872.2.t.k	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}+4\zeta_{6}q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
1872.2.t.l	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2q^{5}+\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+(4+\cdots)q^{13}+\cdots\)
1872.2.t.m	$1872$	$2$	1872.t	13.c	$3$	$2$	$1$	$14.948$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3q^{5}-4\zeta_{6}q^{7}+(-3-\zeta_{6})q^{13}+\cdots\)
1872.2.t.n	$1872$	$2$	1872.t	13.c	$3$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(-2+\cdots)q^{11}+\cdots\)
1872.2.t.o	$1872$	$2$	1872.t	13.c	$3$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}+2\beta _{2}q^{7}-2\beta _{1}q^{11}+(3-\beta _{2}+\cdots)q^{13}+\cdots\)
1872.2.t.p	$1872$	$2$	1872.t	13.c	$3$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{5}-\beta _{1}q^{7}+(-\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1872.2.t.q	$1872$	$2$	1872.t	13.c	$3$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{5}+(\beta _{1}+\beta _{2})q^{7}+(1-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
1872.2.t.r	$1872$	$2$	1872.t	13.c	$3$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{3})q^{5}+(-2-\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
1872.2.t.s	$1872$	$2$	1872.t	13.c	$3$	$4$	$2$	$14.948$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}-\beta _{1}q^{11}+\cdots\)
1872.2.t.t	$1872$	$2$	1872.t	13.c	$3$	$6$	$3$	$14.948$	6.0.27870912.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+\beta _{5}q^{11}+\cdots\)
1872.2.t.u	$1872$	$2$	1872.t	13.c	$3$	$6$	$3$	$14.948$	6.0.2101707.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(2+\beta _{4}-2\beta _{5})q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
1872.2.t.v	$1872$	$2$	1872.t	13.c	$3$	$6$	$3$	$14.948$	6.0.27870912.1	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)

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

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