Space of modular forms of level 882, weight 2, and Character 882.e

• Label: 882.2.e
• Level: $882$
• Weight: $2$
• Character orbit: 882.e
• Rep. character: $\chi_{882}(373,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $20$
• Sturm bound: $336$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(336\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

	Total	New	Old
Modular forms	368	80	288
Cusp forms	304	80	224
Eisenstein series	64	0	64

Trace form

80 * q + 80 * q^4 + 4 * q^5 + 4 * q^6 + 12 * q^9 - 8 * q^11 - 2 * q^13 - 14 * q^15 + 80 * q^16 + 14 * q^17 + 16 * q^18 + 4 * q^19 + 4 * q^20 - 2 * q^23 + 4 * q^24 - 40 * q^25 + 16 * q^26 + 18 * q^29 + 4 * q^31 + 40 * q^33 + 12 * q^36 - 2 * q^37 + 12 * q^38 - 16 * q^39 + 6 * q^41 - 2 * q^43 - 8 * q^44 - 38 * q^45 + 6 * q^46 - 12 * q^47 - 34 * q^51 - 2 * q^52 - 32 * q^53 - 14 * q^54 + 12 * q^55 - 30 * q^57 - 6 * q^58 - 44 * q^59 - 14 * q^60 + 16 * q^61 - 44 * q^62 + 80 * q^64 + 4 * q^65 + 16 * q^66 + 28 * q^67 + 14 * q^68 - 38 * q^69 - 76 * q^71 + 16 * q^72 + 28 * q^73 + 6 * q^74 - 76 * q^75 + 4 * q^76 - 56 * q^78 + 64 * q^79 + 4 * q^80 - 4 * q^81 - 16 * q^83 - 24 * q^85 - 20 * q^86 - 4 * q^87 + 36 * q^89 - 2 * q^90 - 2 * q^92 + 70 * q^93 + 24 * q^94 + 84 * q^95 + 4 * q^96 - 2 * q^97 + 34 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.2.e.a	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					126.2.f.b	$2$	$0$	\(-2\)	\(-3\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
882.2.e.b	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					126.2.f.a	$2$	$0$	\(-2\)	\(-3\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
882.2.e.c	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					126.2.e.a	$2$	$0$	\(-2\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
882.2.e.d	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					126.2.f.a	$2$	$0$	\(-2\)	\(3\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
882.2.e.e	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					126.2.f.b	$2$	$0$	\(-2\)	\(3\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
882.2.e.f	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None		✓			882.2.f.b	$2$	$0$	\(2\)	\(-3\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
882.2.e.g	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					18.2.c.a	$2$	$0$	\(2\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{6}+\cdots\)
882.2.e.h	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					126.2.e.b	$2$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
882.2.e.i	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None					18.2.c.a	$2$	$0$	\(2\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{6}+\cdots\)
882.2.e.j	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	\(\Q(\sqrt{-3}) \)	None		✓			882.2.f.b	$2$	$0$	\(2\)	\(3\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
882.2.e.k	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					126.2.f.d	$2$	$0$	\(-4\)	\(-2\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
882.2.e.l	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					126.2.f.d	$2$	$0$	\(-4\)	\(2\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
882.2.e.m	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.2.f.c	$2$	$0$	\(4\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots\)
882.2.e.n	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.2.f.c	$2$	$0$	\(4\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.2.e.o	$882$	$2$	882.e	63.h	$3$	$6$	$3$	$7.043$	6.0.309123.1	None					126.2.e.c	$2$	$0$	\(-6\)	\(-2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(\beta _{2}+\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
882.2.e.p	$882$	$2$	882.e	63.h	$3$	$6$	$3$	$7.043$	6.0.309123.1	None					126.2.e.d	$2$	$0$	\(6\)	\(2\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+q^{4}+\cdots\)
882.2.e.q	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	\(\Q(\zeta_{24})\)	None		✓			882.2.f.s	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(\beta_{7}+\beta_{3})q^{3}+q^{4}-\beta_{7} q^{5}+\cdots\)
882.2.e.r	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	8.0.\(\cdots\).2	None		✓			882.2.f.r	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-\beta _{3}q^{3}+q^{4}+(-\beta _{5}-\beta _{6})q^{5}+\cdots\)
882.2.e.s	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	\(\Q(\zeta_{24})\)	None		✓			882.2.f.q	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta_{7}+\beta_{6}+\cdots-\beta_{3})q^{3}+\cdots\)
882.2.e.t	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	8.0.3317760000.3	None		✓			882.2.f.p	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(\beta _{5}-\beta _{6})q^{3}+q^{4}+(2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(882, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)