Space of modular forms of level 1629, weight 2, and trivial character

• Label: 1629.2.a
• Level: $1629$
• Weight: $2$
• Character orbit: 1629.a
• Rep. character: $\chi_{1629}(1,\cdot)$
• Character field: $\Q$
• Dimension: $75$
• Newform subspaces: $9$
• Sturm bound: $364$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1629 = 3^{2} \cdot 181 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1629.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(364\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1629))\).

	Total	New	Old
Modular forms	186	75	111
Cusp forms	179	75	104
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.

\(3\)	\(181\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(20\)
\(-\)	\(+\)	\(-\)	\(25\)
\(-\)	\(-\)	\(+\)	\(20\)
Plus space		\(+\)	\(30\)
Minus space		\(-\)	\(45\)

Trace form

75 * q + q^2 + 77 * q^4 + 2 * q^5 + 3 * q^8 + 4 * q^10 + 4 * q^11 - 4 * q^13 + 2 * q^14 + 81 * q^16 - 8 * q^17 + 10 * q^19 + 8 * q^23 + 57 * q^25 - 18 * q^26 + 18 * q^28 + 6 * q^29 - 2 * q^31 + 17 * q^32 + 8 * q^34 + 4 * q^35 - 4 * q^37 + 28 * q^38 - 18 * q^41 + 10 * q^43 + 30 * q^44 - 22 * q^46 - 2 * q^47 + 85 * q^49 + 3 * q^50 - 6 * q^52 - 8 * q^53 - 8 * q^55 + 50 * q^56 + 2 * q^58 - 8 * q^59 + 2 * q^61 - 4 * q^62 + 89 * q^64 + 32 * q^65 + 2 * q^67 + 4 * q^68 - 46 * q^70 - 12 * q^71 - 26 * q^73 + 44 * q^74 - 10 * q^76 - 16 * q^77 + 4 * q^79 - 20 * q^80 - 24 * q^82 - 34 * q^83 - 16 * q^85 + 14 * q^86 - 18 * q^88 + 14 * q^89 + 8 * q^91 + 68 * q^92 - 40 * q^94 + 8 * q^95 + 2 * q^97 - 51 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1629))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	181
1629.2.a.a	$1629$	$2$	1629.a	1.a	$1$	$3$	$3$	$13.008$	\(\Q(\zeta_{14})^+\)	None	✓				543.2.a.a	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
1629.2.a.b	$1629$	$2$	1629.a	1.a	$1$	$5$	$5$	$13.008$	5.5.170701.1	None	✓				543.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1629.2.a.c	$1629$	$2$	1629.a	1.a	$1$	$5$	$5$	$13.008$	5.5.24217.1	None	✓				181.2.a.a	$1$	$0$	\(3\)	\(0\)	\(5\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(1-\beta _{2}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
1629.2.a.d	$1629$	$2$	1629.a	1.a	$1$	$7$	$7$	$13.008$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				543.2.a.c	$1$	$0$	\(4\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1629.2.a.e	$1629$	$2$	1629.a	1.a	$1$	$8$	$8$	$13.008$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				543.2.a.d	$1$	$1$	\(-3\)	\(0\)	\(-5\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1629.2.a.f	$1629$	$2$	1629.a	1.a	$1$	$8$	$8$	$13.008$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		543.2.a.e	$1$	$0$	\(-3\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}+(2+\beta _{1}+\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1629.2.a.g	$1629$	$2$	1629.a	1.a	$1$	$9$	$9$	$13.008$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		181.2.a.b	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1629.2.a.h	$1629$	$2$	1629.a	1.a	$1$	$10$	$10$	$13.008$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	1629.2.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-10\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
1629.2.a.i	$1629$	$2$	1629.a	1.a	$1$	$20$	$20$	$13.008$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	1629.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{14}q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1629))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1629)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(181))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(543))\)\(^{\oplus 2}\)