Space of modular forms of level 1922, weight 2, and trivial character

• Label: 1922.2.a
• Level: $1922$
• Weight: $2$
• Character orbit: 1922.a
• Rep. character: $\chi_{1922}(1,\cdot)$
• Character field: $\Q$
• Dimension: $77$
• Newform subspaces: $20$
• Sturm bound: $496$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1922 = 2 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1922.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(496\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1922))\).

	Total	New	Old
Modular forms	280	77	203
Cusp forms	217	77	140
Eisenstein series	63	0	63

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

\(2\)	\(31\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(64\)	\(17\)	\(47\)		\(49\)	\(17\)	\(32\)		\(15\)	\(0\)	\(15\)
\(+\)	\(-\)	\(-\)		\(76\)	\(21\)	\(55\)		\(60\)	\(21\)	\(39\)		\(16\)	\(0\)	\(16\)
\(-\)	\(+\)	\(-\)		\(72\)	\(25\)	\(47\)		\(56\)	\(25\)	\(31\)		\(16\)	\(0\)	\(16\)
\(-\)	\(-\)	\(+\)		\(68\)	\(14\)	\(54\)		\(52\)	\(14\)	\(38\)		\(16\)	\(0\)	\(16\)
Plus space		\(+\)		\(132\)	\(31\)	\(101\)		\(101\)	\(31\)	\(70\)		\(31\)	\(0\)	\(31\)
Minus space		\(-\)		\(148\)	\(46\)	\(102\)		\(116\)	\(46\)	\(70\)		\(32\)	\(0\)	\(32\)

Trace form

77 * q + q^2 - 2 * q^3 + 77 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + q^8 + 81 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 + 4 * q^14 + 12 * q^15 + 77 * q^16 + 6 * q^17 + 5 * q^18 + 4 * q^19 + 2 * q^20 - 4 * q^21 - 6 * q^22 - 8 * q^23 + 2 * q^24 + 67 * q^25 - 4 * q^26 - 8 * q^27 - 4 * q^28 + 4 * q^29 - 12 * q^30 + q^32 + 6 * q^34 + 81 * q^36 - 20 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 14 * q^41 + 4 * q^42 - 6 * q^43 + 6 * q^44 + 10 * q^45 - 8 * q^46 - 4 * q^47 - 2 * q^48 + 93 * q^49 + 15 * q^50 - 20 * q^51 + 8 * q^54 + 12 * q^55 + 4 * q^56 + 8 * q^57 - 8 * q^58 + 16 * q^59 + 12 * q^60 + 8 * q^61 - 12 * q^63 + 77 * q^64 - 32 * q^65 - 8 * q^66 - 4 * q^67 + 6 * q^68 - 8 * q^69 - 16 * q^71 + 5 * q^72 + 10 * q^73 - 14 * q^75 + 4 * q^76 + 12 * q^77 - 28 * q^78 + 4 * q^79 + 2 * q^80 + 61 * q^81 + 18 * q^82 - 14 * q^83 - 4 * q^84 + 12 * q^85 - 10 * q^86 - 20 * q^87 - 6 * q^88 - 6 * q^89 - 30 * q^90 + 4 * q^91 - 8 * q^92 + 16 * q^94 + 2 * q^96 - 10 * q^97 - 7 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1922))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	31
1922.2.a.a	$1922$	$2$	1922.a	1.a	$1$	$1$	$1$	$15.347$	\(\Q\)	None	✓				62.2.c.a	$1$	$2$	\(-1\)	\(-1\)	\(-3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
1922.2.a.b	$1922$	$2$	1922.a	1.a	$1$	$1$	$1$	$15.347$	\(\Q\)	None	✓				62.2.c.a	$1$	$1$	\(-1\)	\(1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
1922.2.a.c	$1922$	$2$	1922.a	1.a	$1$	$1$	$1$	$15.347$	\(\Q\)	None	✓				62.2.c.b	$1$	$1$	\(1\)	\(-3\)	\(1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}-3q^{7}+\cdots\)
1922.2.a.d	$1922$	$2$	1922.a	1.a	$1$	$1$	$1$	$15.347$	\(\Q\)	None	✓				62.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
1922.2.a.e	$1922$	$2$	1922.a	1.a	$1$	$1$	$1$	$15.347$	\(\Q\)	None	✓				62.2.c.b	$1$	$0$	\(1\)	\(3\)	\(1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}-3q^{7}+\cdots\)
1922.2.a.f	$1922$	$2$	1922.a	1.a	$1$	$2$	$2$	$15.347$	\(\Q(\sqrt{3}) \)	None	✓				62.2.a.b	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}+2\beta q^{5}+\cdots\)
1922.2.a.g	$1922$	$2$	1922.a	1.a	$1$	$2$	$2$	$15.347$	\(\Q(\sqrt{10}) \)	None	✓	✓			1922.2.a.g	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-2q^{5}-\beta q^{6}+2q^{7}+\cdots\)
1922.2.a.h	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\zeta_{15})^+\)	None	✓				62.2.g.b	$1$	$1$	\(-4\)	\(-6\)	\(3\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2-\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
1922.2.a.i	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	4.4.8725.1	None	✓				62.2.d.b	$1$	$1$	\(-4\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
1922.2.a.j	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\zeta_{16})^+\)	None	✓	✓			1922.2.a.j	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
1922.2.a.k	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	✓			1922.2.a.k	$2$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{3})q^{5}-\beta _{1}q^{6}+\cdots\)
1922.2.a.l	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	4.4.8725.1	None	✓				62.2.d.b	$1$	$0$	\(-4\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
1922.2.a.m	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\zeta_{15})^+\)	None	✓				62.2.g.b	$1$	$0$	\(-4\)	\(6\)	\(3\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(2+\beta _{3})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots\)
1922.2.a.n	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	4.4.4525.1	None	✓				62.2.d.a	$1$	$1$	\(4\)	\(-3\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
1922.2.a.o	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\zeta_{15})^+\)	None	✓				62.2.g.a	$1$	$1$	\(4\)	\(-2\)	\(-1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+(-1-\beta _{2}-2\beta _{3})q^{5}+\cdots\)
1922.2.a.p	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\zeta_{16})^+\)	None	✓	✓			1922.2.a.p	$2$	$1$	\(4\)	\(0\)	\(-8\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(\beta _{1}+\beta _{3})q^{3}+q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
1922.2.a.q	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	\(\Q(\zeta_{15})^+\)	None	✓				62.2.g.a	$1$	$0$	\(4\)	\(2\)	\(-1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{3}q^{3}+q^{4}+(-1-\beta _{2}-2\beta _{3})q^{5}+\cdots\)
1922.2.a.r	$1922$	$2$	1922.a	1.a	$1$	$4$	$4$	$15.347$	4.4.4525.1	None	✓				62.2.d.a	$1$	$0$	\(4\)	\(3\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
1922.2.a.s	$1922$	$2$	1922.a	1.a	$1$	$8$	$8$	$15.347$	\(\Q(\zeta_{32})^+\)	None	✓	✓	✓		1922.2.a.s	$2$	$1$	\(-8\)	\(0\)	\(0\)	\(-16\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-\beta _{5}-\beta _{7})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1922.2.a.t	$1922$	$2$	1922.a	1.a	$1$	$16$	$16$	$15.347$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		1922.2.a.t	$2$	$0$	\(16\)	\(0\)	\(16\)	\(16\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1922))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1922)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(961))\)\(^{\oplus 2}\)