Space of modular forms of level 1606, weight 2, and trivial character

• Label: 1606.2.a
• Level: $1606$
• Weight: $2$
• Character orbit: 1606.a
• Rep. character: $\chi_{1606}(1,\cdot)$
• Character field: $\Q$
• Dimension: $59$
• Newform subspaces: $9$
• Sturm bound: $444$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1606 = 2 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1606.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(444\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1606))\).

	Total	New	Old
Modular forms	226	59	167
Cusp forms	219	59	160
Eisenstein series	7	0	7

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

\(2\)	\(11\)	\(73\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(+\)	\(-\)	$-$	\(6\)
\(+\)	\(-\)	\(+\)	$-$	\(10\)
\(+\)	\(-\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(+\)	$-$	\(8\)
\(-\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(-\)	$-$	\(12\)
Plus space			\(+\)	\(23\)
Minus space			\(-\)	\(36\)

Trace form

\( 59 q - q^{2} + 59 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{7} - q^{8} + 59 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1606))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	11	73
1606.2.a.a	$1606$	$2$	1606.a	1.a	$1$	$3$	$3$	$12.824$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(3\)	\(-2\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1606.2.a.b	$1606$	$2$	1606.a	1.a	$1$	$4$	$4$	$12.824$	4.4.43569.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(-2\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
1606.2.a.c	$1606$	$2$	1606.a	1.a	$1$	$5$	$5$	$12.824$	5.5.170701.1	None	✓	$1$	$1$	\(-5\)	\(-1\)	\(-4\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
1606.2.a.d	$1606$	$2$	1606.a	1.a	$1$	$6$	$6$	$12.824$	6.6.26885473.1	None	✓	$1$	$0$	\(-6\)	\(-2\)	\(3\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1606.2.a.e	$1606$	$2$	1606.a	1.a	$1$	$6$	$6$	$12.824$	6.6.7342612.1	None	✓	$1$	$1$	\(6\)	\(-4\)	\(-4\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1606.2.a.f	$1606$	$2$	1606.a	1.a	$1$	$8$	$8$	$12.824$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(3\)	\(3\)	\(8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}+\beta _{6})q^{5}+\cdots\)
1606.2.a.g	$1606$	$2$	1606.a	1.a	$1$	$8$	$8$	$12.824$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(5\)	\(5\)	\(-6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(1-\beta _{7})q^{5}+\cdots\)
1606.2.a.h	$1606$	$2$	1606.a	1.a	$1$	$9$	$9$	$12.824$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(1\)	\(-4\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
1606.2.a.i	$1606$	$2$	1606.a	1.a	$1$	$10$	$10$	$12.824$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-10\)	\(0\)	\(9\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{4})q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1606))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1606)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(803))\)\(^{\oplus 2}\)