Space of modular forms of level 833, weight 2, and trivial character

• Label: 833.2.a
• Level: $833$
• Weight: $2$
• Character orbit: 833.a
• Rep. character: $\chi_{833}(1,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $11$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(833))\).

	Total	New	Old
Modular forms	92	54	38
Cusp forms	77	54	23
Eisenstein series	15	0	15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(11\)
\(+\)	\(-\)	$-$	\(15\)
\(-\)	\(+\)	$-$	\(17\)
\(-\)	\(-\)	$+$	\(11\)
Plus space		\(+\)	\(22\)
Minus space		\(-\)	\(32\)

Trace form

\( 54 q - 2 q^{2} + 50 q^{4} - 6 q^{8} + 50 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(833))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	17
833.2.a.a	$833$	$2$	833.a	1.a	$1$	$1$	$1$	$6.652$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
833.2.a.b	$833$	$2$	833.a	1.a	$1$	$3$	$3$	$6.652$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
833.2.a.c	$833$	$2$	833.a	1.a	$1$	$3$	$3$	$6.652$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
833.2.a.d	$833$	$2$	833.a	1.a	$1$	$4$	$4$	$6.652$	4.4.1957.1	None	✓	$1$	$1$	\(-1\)	\(-4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.a.e	$833$	$2$	833.a	1.a	$1$	$4$	$4$	$6.652$	4.4.9301.1	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
833.2.a.f	$833$	$2$	833.a	1.a	$1$	$4$	$4$	$6.652$	4.4.1957.1	None	✓	$1$	$0$	\(-1\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
833.2.a.g	$833$	$2$	833.a	1.a	$1$	$5$	$5$	$6.652$	5.5.453749.1	None	✓	$1$	$0$	\(2\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots\)
833.2.a.h	$833$	$2$	833.a	1.a	$1$	$7$	$7$	$6.652$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.a.i	$833$	$2$	833.a	1.a	$1$	$7$	$7$	$6.652$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.a.j	$833$	$2$	833.a	1.a	$1$	$8$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-8\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
833.2.a.k	$833$	$2$	833.a	1.a	$1$	$8$	$8$	$6.652$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(8\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(833))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(833)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 2}\)