Space of modular forms of level 1881, weight 2, and trivial character

• Label: 1881.2.a
• Level: $1881$
• Weight: $2$
• Character orbit: 1881.a
• Rep. character: $\chi_{1881}(1,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $18$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1881.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1881))\).

	Total	New	Old
Modular forms	248	74	174
Cusp forms	233	74	159
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.

\(3\)	\(11\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	\(15\)
Plus space			\(+\)	\(32\)
Minus space			\(-\)	\(42\)

Trace form

\( 74 q - 2 q^{2} + 72 q^{4} - 2 q^{5} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1881))\) 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	11	19
1881.2.a.a	$1881$	$2$	1881.a	1.a	$1$	$1$	$1$	$15.020$	\(\Q\)	None	✓				627.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}+2q^{7}+q^{11}+q^{13}+\cdots\)
1881.2.a.b	$1881$	$2$	1881.a	1.a	$1$	$1$	$1$	$15.020$	\(\Q\)	None	✓				627.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{7}-q^{11}-q^{13}+4q^{16}+\cdots\)
1881.2.a.c	$1881$	$2$	1881.a	1.a	$1$	$1$	$1$	$15.020$	\(\Q\)	None	✓				209.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots\)
1881.2.a.d	$1881$	$2$	1881.a	1.a	$1$	$2$	$2$	$15.020$	\(\Q(\sqrt{2}) \)	None	✓				209.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{5}+(-2+\beta )q^{7}-2\beta q^{8}+\cdots\)
1881.2.a.e	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	\(\Q(\zeta_{14})^+\)	None	✓				627.2.a.f	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1881.2.a.f	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	3.3.169.1	None	✓				627.2.a.g	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1881.2.a.g	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	\(\Q(\zeta_{14})^+\)	None	✓				627.2.a.d	$1$	$0$	\(2\)	\(0\)	\(7\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
1881.2.a.h	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	3.3.169.1	None	✓				627.2.a.c	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1881.2.a.i	$1881$	$2$	1881.a	1.a	$1$	$3$	$3$	$15.020$	3.3.321.1	None	✓				627.2.a.e	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1881.2.a.j	$1881$	$2$	1881.a	1.a	$1$	$4$	$4$	$15.020$	4.4.23377.1	None	✓		✓		627.2.a.h	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
1881.2.a.k	$1881$	$2$	1881.a	1.a	$1$	$5$	$5$	$15.020$	5.5.246832.1	None	✓				209.2.a.c	$1$	$0$	\(-2\)	\(0\)	\(5\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
1881.2.a.l	$1881$	$2$	1881.a	1.a	$1$	$5$	$5$	$15.020$	5.5.2179633.1	None	✓				627.2.a.i	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1881.2.a.m	$1881$	$2$	1881.a	1.a	$1$	$5$	$5$	$15.020$	5.5.1920025.1	None	✓				627.2.a.j	$1$	$0$	\(-1\)	\(0\)	\(-7\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1881.2.a.n	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	1881.2.a.n	$1$	$1$	\(-2\)	\(0\)	\(-8\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1881.2.a.o	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	1881.2.a.o	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1881.2.a.p	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		209.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(10\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\beta _{4}q^{5}+\cdots\)
1881.2.a.q	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	1881.2.a.o	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1881.2.a.r	$1881$	$2$	1881.a	1.a	$1$	$7$	$7$	$15.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	1881.2.a.n	$1$	$0$	\(2\)	\(0\)	\(8\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}+(1-\beta _{3})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1881))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1881)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 2}\)