Space of modular forms of level 1881, weight 4, and trivial character

• Label: 1881.4.a
• Level: $1881$
• Weight: $4$
• Character orbit: 1881.a
• Rep. character: $\chi_{1881}(1,\cdot)$
• Character field: $\Q$
• Dimension: $226$
• Newform subspaces: $16$
• Sturm bound: $960$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1881.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(960\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1881))\).

	Total	New	Old
Modular forms	728	226	502
Cusp forms	712	226	486
Eisenstein series	16	0	16

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
\(+\)	\(+\)	\(+\)	\(+\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)	\(23\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(23\)
\(-\)	\(+\)	\(+\)	\(-\)	\(32\)
\(-\)	\(+\)	\(-\)	\(+\)	\(37\)
\(-\)	\(-\)	\(+\)	\(+\)	\(35\)
\(-\)	\(-\)	\(-\)	\(-\)	\(30\)
Plus space			\(+\)	\(118\)
Minus space			\(-\)	\(108\)

Trace form

226 * q - 4 * q^2 + 912 * q^4 - 28 * q^5 - 36 * q^8 - 40 * q^10 - 44 * q^11 - 144 * q^13 + 180 * q^14 + 3768 * q^16 + 88 * q^17 - 360 * q^20 - 160 * q^23 + 5662 * q^25 + 236 * q^26 - 864 * q^28 + 96 * q^29 + 212 * q^31 - 292 * q^32 - 816 * q^34 + 104 * q^35 - 88 * q^37 - 228 * q^38 - 1752 * q^40 - 136 * q^41 - 488 * q^43 - 1056 * q^44 - 312 * q^46 - 24 * q^47 + 12162 * q^49 + 908 * q^50 + 1904 * q^52 - 404 * q^53 + 44 * q^55 + 2356 * q^56 + 3652 * q^58 + 3508 * q^59 - 800 * q^61 + 5492 * q^62 + 17008 * q^64 - 1616 * q^65 - 1428 * q^67 + 4764 * q^68 + 1988 * q^70 - 1316 * q^71 - 792 * q^73 - 468 * q^74 - 792 * q^77 - 1120 * q^79 - 10136 * q^80 + 4000 * q^82 + 2576 * q^83 - 5080 * q^85 + 6160 * q^86 - 5624 * q^89 + 272 * q^91 - 196 * q^92 - 3928 * q^94 - 6240 * q^97 + 116 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1881))\) 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
1881.4.a.a	$1881$	$4$	1881.a	1.a	$1$	$8$	$8$	$110.983$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				209.4.a.a	$1$	$1$	\(0\)	\(0\)	\(12\)	\(-59\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(2-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
1881.4.a.b	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				627.4.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1881.4.a.c	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				627.4.a.d	$1$	$0$	\(0\)	\(0\)	\(21\)	\(10\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1}-\beta _{9})q^{5}+\cdots\)
1881.4.a.d	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				627.4.a.c	$1$	$1$	\(0\)	\(0\)	\(21\)	\(-38\)		$-$	$+$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(2-\beta _{7})q^{5}+\cdots\)
1881.4.a.e	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				209.4.a.b	$1$	$1$	\(6\)	\(0\)	\(10\)	\(-53\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1881.4.a.f	$1881$	$4$	1881.a	1.a	$1$	$10$	$10$	$110.983$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				627.4.a.a	$1$	$0$	\(8\)	\(0\)	\(41\)	\(-52\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(5+\beta _{2}+\beta _{3})q^{4}+(4+\cdots)q^{5}+\cdots\)
1881.4.a.g	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		627.4.a.g	$1$	$1$	\(-6\)	\(0\)	\(-49\)	\(-18\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(-4+\beta _{4}+\cdots)q^{5}+\cdots\)
1881.4.a.h	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		627.4.a.h	$1$	$1$	\(-6\)	\(0\)	\(-29\)	\(60\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(6+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1881.4.a.i	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				627.4.a.f	$1$	$0$	\(-6\)	\(0\)	\(-9\)	\(46\)		$-$	$+$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1881.4.a.j	$1881$	$4$	1881.a	1.a	$1$	$12$	$12$	$110.983$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				627.4.a.e	$1$	$0$	\(2\)	\(0\)	\(-29\)	\(-4\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-2+\beta _{4})q^{5}+\cdots\)
1881.4.a.k	$1881$	$4$	1881.a	1.a	$1$	$13$	$13$	$110.983$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓		✓		209.4.a.c	$1$	$0$	\(2\)	\(0\)	\(-8\)	\(39\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
1881.4.a.l	$1881$	$4$	1881.a	1.a	$1$	$15$	$15$	$110.983$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		209.4.a.d	$1$	$0$	\(-4\)	\(0\)	\(-10\)	\(73\)		$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
1881.4.a.m	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		None	✓	✓	✓	✓	1881.4.a.m	$1$	$1$	\(-4\)	\(0\)	\(-40\)	\(14\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
1881.4.a.n	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		None	✓	✓	✓	✓	1881.4.a.n	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(-14\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
1881.4.a.o	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		None	✓	✓	✓	✓	1881.4.a.n	$1$	$0$	\(4\)	\(0\)	\(0\)	\(-14\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
1881.4.a.p	$1881$	$4$	1881.a	1.a	$1$	$23$	$23$	$110.983$		None	✓	✓	✓	✓	1881.4.a.m	$1$	$0$	\(4\)	\(0\)	\(40\)	\(14\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1881))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1881)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 2}\)