Space of modular forms of level 2736, weight 3, and Character 2736.o

• Label: 2736.3.o
• Level: $2736$
• Weight: $3$
• Character orbit: 2736.o
• Rep. character: $\chi_{2736}(721,\cdot)$
• Character field: $\Q$
• Dimension: $99$
• Newform subspaces: $18$
• Sturm bound: $1440$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2736.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1440\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

	Total	New	Old
Modular forms	984	101	883
Cusp forms	936	99	837
Eisenstein series	48	2	46

Trace form

\( 99 q + 2 q^{5} + 18 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2736.3.o.a	$2736$	$3$	2736.o	19.b	$2$	$1$	$1$	$74.551$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(9\)	\(5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{5}+5q^{7}+3q^{11}-15q^{17}+19q^{19}+\cdots\)
2736.3.o.b	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(-22\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-7q^{5}-11q^{7}+3q^{11}+2\beta q^{13}+\cdots\)
2736.3.o.c	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-4-\beta )q^{5}+(-4+3\beta )q^{7}+(-4+\cdots)q^{11}+\cdots\)
2736.3.o.d	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{-13}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}+5q^{7}-10q^{11}-\beta q^{13}-15q^{17}+\cdots\)
2736.3.o.e	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(20\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}+10q^{7}+10q^{11}-7\zeta_{6}q^{13}+\cdots\)
2736.3.o.f	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{19}) \)	\(\Q(\sqrt{-19}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-5q^{7}+5\beta q^{11}+7\beta q^{17}+\cdots\)
2736.3.o.g	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{7}-\zeta_{6}q^{13}+(13-\zeta_{6})q^{19}-5^{2}q^{25}+\cdots\)
2736.3.o.h	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-10\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}-5q^{7}+5q^{11}-2\beta q^{13}+5^{2}q^{17}+\cdots\)
2736.3.o.i	$2736$	$3$	2736.o	19.b	$2$	$2$	$2$	$74.551$	\(\Q(\sqrt{-29}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{5}+q^{7}+14q^{11}+\beta q^{13}-23q^{17}+\cdots\)
2736.3.o.j	$2736$	$3$	2736.o	19.b	$2$	$4$	$4$	$74.551$	\(\Q(\sqrt{-7}, \sqrt{10})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+2q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
2736.3.o.k	$2736$	$3$	2736.o	19.b	$2$	$4$	$4$	$74.551$	\(\Q(\sqrt{3}, \sqrt{19})\)	\(\Q(\sqrt{-19}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$2^{3}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+(3+\beta _{3})q^{7}+\beta _{2}q^{11}+(2\beta _{1}+\cdots)q^{17}+\cdots\)
2736.3.o.l	$2736$	$3$	2736.o	19.b	$2$	$4$	$4$	$74.551$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(-34\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3+\beta _{1})q^{5}+(-9-\beta _{1})q^{7}+(-3+\cdots)q^{11}+\cdots\)
2736.3.o.m	$2736$	$3$	2736.o	19.b	$2$	$6$	$6$	$74.551$	6.0.219615408.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{2}q^{7}+(-4-\beta _{2})q^{11}+\cdots\)
2736.3.o.n	$2736$	$3$	2736.o	19.b	$2$	$8$	$8$	$74.551$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(12\)	$2^{8}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
2736.3.o.o	$2736$	$3$	2736.o	19.b	$2$	$8$	$8$	$74.551$	8.0.\(\cdots\).9	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-1-\beta _{7})q^{7}+(-\beta _{1}-\beta _{5}+\cdots)q^{11}+\cdots\)
2736.3.o.p	$2736$	$3$	2736.o	19.b	$2$	$8$	$8$	$74.551$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(6\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{4})q^{5}+(1-\beta _{3})q^{7}+(-4-\beta _{4}+\cdots)q^{11}+\cdots\)
2736.3.o.q	$2736$	$3$	2736.o	19.b	$2$	$20$	$20$	$74.551$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{32}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{5}+(1-\beta _{3})q^{7}+\beta _{14}q^{11}+\cdots\)
2736.3.o.r	$2736$	$3$	2736.o	19.b	$2$	$20$	$20$	$74.551$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{37}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)