Space of modular forms of level 833, weight 2, and Character 833.e

• Label: 833.2.e
• Level: $833$
• Weight: $2$
• Character orbit: 833.e
• Rep. character: $\chi_{833}(18,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $108$
• Newform subspaces: $12$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(833, [\chi])\).

	Total	New	Old
Modular forms	184	108	76
Cusp forms	152	108	44
Eisenstein series	32	0	32

Trace form

108 * q + 4 * q^2 + 2 * q^3 - 52 * q^4 + 4 * q^5 - 12 * q^8 - 60 * q^9 - 6 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 - 24 * q^15 - 32 * q^16 + 4 * q^17 + 32 * q^18 - 6 * q^19 - 48 * q^20 - 40 * q^22 + 32 * q^23 - 62 * q^25 - 8 * q^26 - 16 * q^27 - 24 * q^29 + 32 * q^30 + 6 * q^31 + 36 * q^32 - 26 * q^33 - 8 * q^34 + 112 * q^36 - 18 * q^37 - 30 * q^38 - 20 * q^39 - 32 * q^40 + 12 * q^41 + 36 * q^43 + 14 * q^44 + 4 * q^45 + 12 * q^46 - 2 * q^47 - 52 * q^48 - 40 * q^50 + 2 * q^52 + 8 * q^53 + 28 * q^54 + 28 * q^55 + 24 * q^57 + 56 * q^58 - 2 * q^59 + 56 * q^60 - 36 * q^62 - 92 * q^64 + 26 * q^65 - 4 * q^67 + 12 * q^68 - 56 * q^69 + 28 * q^71 + 64 * q^72 + 28 * q^73 - 8 * q^74 - 12 * q^75 + 44 * q^76 + 20 * q^78 - 8 * q^79 - 10 * q^80 - 74 * q^81 + 40 * q^82 - 24 * q^83 - 64 * q^86 + 2 * q^87 + 52 * q^88 - 24 * q^89 - 92 * q^90 + 16 * q^92 - 14 * q^93 - 26 * q^94 + 60 * q^95 + 24 * q^96 + 28 * q^97 - 84 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(833, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
833.2.e.a	$833$	$2$	833.e	7.c	$3$	$2$	$1$	$6.652$	\(\Q(\sqrt{-3}) \)	None					17.2.a.a	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}+3q^{8}+\cdots\)
833.2.e.b	$833$	$2$	833.e	7.c	$3$	$2$	$1$	$6.652$	\(\Q(\sqrt{-3}) \)	None					17.2.a.a	$2$	$0$	\(1\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}+3q^{8}+\cdots\)
833.2.e.c	$833$	$2$	833.e	7.c	$3$	$6$	$3$	$6.652$	6.0.64827.1	None					119.2.e.a	$2$	$0$	\(1\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.e.d	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	8.0.310217769.2	None		✓			833.2.a.d	$2$	$0$	\(1\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}-\beta _{6})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
833.2.e.e	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	8.0.7007196681.1	None					119.2.a.a	$2$	$0$	\(1\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{3}+\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.e.f	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	8.0.7007196681.1	None					119.2.a.a	$2$	$0$	\(1\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3}-\beta _{7})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.e.g	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	8.0.310217769.2	None		✓			833.2.a.d	$2$	$0$	\(1\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
833.2.e.h	$833$	$2$	833.e	7.c	$3$	$10$	$5$	$6.652$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					119.2.a.b	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(\beta _{3}-\beta _{7}-\beta _{8})q^{3}+(\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
833.2.e.i	$833$	$2$	833.e	7.c	$3$	$10$	$5$	$6.652$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					119.2.a.b	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(-\beta _{3}+\beta _{7}+\beta _{8})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
833.2.e.j	$833$	$2$	833.e	7.c	$3$	$14$	$7$	$6.652$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					119.2.e.b	$2$	$0$	\(-3\)	\(1\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{13}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.e.k	$833$	$2$	833.e	7.c	$3$	$16$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			833.2.a.j	$2$	$0$	\(2\)	\(-8\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{6}+\beta _{10}+\beta _{14}+\cdots)q^{3}+\cdots\)
833.2.e.l	$833$	$2$	833.e	7.c	$3$	$16$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			833.2.a.j	$2$	$0$	\(2\)	\(8\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1+\beta _{6}-\beta _{10}-\beta _{14})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(833, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(833, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)