Space of modular forms of level 2664, weight 2, and Character 2664.r

• Label: 2664.2.r
• Level: $2664$
• Weight: $2$
• Character orbit: 2664.r
• Rep. character: $\chi_{2664}(433,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $94$
• Newform subspaces: $16$
• Sturm bound: $912$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2664.r (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(912\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2664, [\chi])\).

	Total	New	Old
Modular forms	944	94	850
Cusp forms	880	94	786
Eisenstein series	64	0	64

Trace form

94 * q + q^5 - 2 * q^7 - 8 * q^11 - 4 * q^13 + q^17 + 2 * q^19 - 40 * q^25 + 2 * q^29 + 8 * q^31 + 6 * q^35 - q^37 - 19 * q^41 + 8 * q^47 - 53 * q^49 - 4 * q^53 + 12 * q^55 - 2 * q^59 + 3 * q^61 - 4 * q^65 - 10 * q^67 + 6 * q^71 - 4 * q^73 - 4 * q^77 - 22 * q^79 - 10 * q^83 + 6 * q^85 - 3 * q^89 - 26 * q^91 + 14 * q^95 + 30 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2664, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2664.2.r.a	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None					888.2.q.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+7\zeta_{6}q^{13}+(-6+\cdots)q^{17}+\cdots\)
2664.2.r.b	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None					888.2.q.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+4q^{11}-\zeta_{6}q^{13}+\cdots\)
2664.2.r.c	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None					888.2.q.d	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+4\zeta_{6}q^{7}+2\zeta_{6}q^{13}+(7-7\zeta_{6})q^{17}+\cdots\)
2664.2.r.d	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None		✓			2664.2.r.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{7}-6q^{11}+3\zeta_{6}q^{13}+(2-2\zeta_{6})q^{17}+\cdots\)
2664.2.r.e	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None		✓			2664.2.r.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{7}+6q^{11}+3\zeta_{6}q^{13}+(-2+\cdots)q^{17}+\cdots\)
2664.2.r.f	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None					296.2.i.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}-3\zeta_{6}q^{7}-3\zeta_{6}q^{13}+(-1+\cdots)q^{17}+\cdots\)
2664.2.r.g	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	\(\Q(\sqrt{-3}) \)	None					888.2.q.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}-\zeta_{6}q^{7}+2q^{11}-3\zeta_{6}q^{13}+\cdots\)
2664.2.r.h	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.50898483.1	None					888.2.q.h	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{3})q^{5}-\beta _{3}q^{7}+(\beta _{2}-\beta _{4})q^{11}+\cdots\)
2664.2.r.i	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.591408.1	None					296.2.i.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{3}-\beta _{4})q^{7}+2\beta _{3}q^{13}+\cdots\)
2664.2.r.j	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.47545083.2	None					888.2.q.g	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{5}-3\beta _{4}q^{7}+(-3-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
2664.2.r.k	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.1415907.1	None					888.2.q.f	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-7\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{3}+\beta _{4})q^{5}+(-\beta _{1}-2\beta _{3}+\cdots)q^{7}+\cdots\)
2664.2.r.l	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.1415907.1	None					888.2.q.e	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2}-2\beta _{4})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2664.2.r.m	$2664$	$2$	2664.r	37.c	$3$	$8$	$4$	$21.272$	\(\Q(\sqrt{-3}, \sqrt{5}, \sqrt{13})\)	None					888.2.q.i	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
2664.2.r.n	$2664$	$2$	2664.r	37.c	$3$	$10$	$5$	$21.272$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					296.2.i.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{6}-\beta _{9})q^{5}+(1-\beta _{7}-\beta _{8}+\cdots)q^{7}+\cdots\)
2664.2.r.o	$2664$	$2$	2664.r	37.c	$3$	$16$	$8$	$21.272$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2664.2.r.o	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{5}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{9})q^{7}+\cdots\)
2664.2.r.p	$2664$	$2$	2664.r	37.c	$3$	$16$	$8$	$21.272$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2664.2.r.o	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{5}+\beta _{11})q^{5}+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2664, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2664, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1332, [\chi])\)\(^{\oplus 2}\)