Space of modular forms of level 201, weight 4, and trivial character

• Label: 201.4.a
• Level: $201$
• Weight: $4$
• Character orbit: 201.a
• Rep. character: $\chi_{201}(1,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $5$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(201))\).

	Total	New	Old
Modular forms	70	34	36
Cusp forms	66	34	32
Eisenstein series	4	0	4

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

\(3\)	\(67\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(19\)	\(9\)	\(10\)		\(18\)	\(9\)	\(9\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(16\)	\(8\)	\(8\)		\(15\)	\(8\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(16\)	\(6\)	\(10\)		\(15\)	\(6\)	\(9\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(19\)	\(11\)	\(8\)		\(18\)	\(11\)	\(7\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(38\)	\(20\)	\(18\)		\(36\)	\(20\)	\(16\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(32\)	\(14\)	\(18\)		\(30\)	\(14\)	\(16\)		\(2\)	\(0\)	\(2\)

Trace form

34 * q - 4 * q^2 + 156 * q^4 + 4 * q^7 - 48 * q^8 + 306 * q^9 - 12 * q^10 + 24 * q^12 - 144 * q^13 + 192 * q^14 - 24 * q^15 + 644 * q^16 - 8 * q^17 - 36 * q^18 + 60 * q^19 - 32 * q^20 + 84 * q^21 - 152 * q^22 + 436 * q^23 - 180 * q^24 + 946 * q^25 - 20 * q^26 + 396 * q^28 - 304 * q^29 - 456 * q^30 - 460 * q^31 + 312 * q^32 + 192 * q^33 - 380 * q^34 - 1440 * q^35 + 1404 * q^36 + 44 * q^37 + 1140 * q^38 + 312 * q^39 + 868 * q^40 + 192 * q^41 + 300 * q^42 + 408 * q^43 - 1024 * q^44 - 1200 * q^46 - 972 * q^47 + 816 * q^48 + 1734 * q^49 + 1828 * q^50 - 864 * q^51 - 836 * q^52 - 184 * q^53 - 472 * q^55 + 1020 * q^56 - 696 * q^57 + 136 * q^58 + 468 * q^59 - 1608 * q^60 - 1128 * q^61 + 20 * q^62 + 36 * q^63 + 4388 * q^64 - 1848 * q^65 - 144 * q^66 + 268 * q^67 - 4076 * q^68 - 72 * q^69 - 4544 * q^70 + 304 * q^71 - 432 * q^72 - 348 * q^73 - 3924 * q^74 - 576 * q^75 + 464 * q^76 + 4584 * q^77 + 1380 * q^78 - 1396 * q^79 - 4032 * q^80 + 2754 * q^81 - 3020 * q^82 - 1048 * q^83 + 2880 * q^84 + 232 * q^85 - 5348 * q^86 - 564 * q^87 - 2008 * q^88 - 2048 * q^89 - 108 * q^90 + 384 * q^91 + 2924 * q^92 + 1836 * q^93 - 176 * q^94 - 976 * q^95 - 1440 * q^96 + 588 * q^97 - 1628 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(201))\) 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	67
201.4.a.a	$201$	$4$	201.a	1.a	$1$	$1$	$1$	$11.859$	\(\Q\)	None	✓	✓			201.4.a.a	$1$	$1$	\(-4\)	\(-3\)	\(-19\)	\(13\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-3q^{3}+8q^{4}-19q^{5}+12q^{6}+\cdots\)
201.4.a.b	$201$	$4$	201.a	1.a	$1$	$6$	$6$	$11.859$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	201.4.a.b	$1$	$1$	\(-5\)	\(18\)	\(-12\)	\(-62\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
201.4.a.c	$201$	$4$	201.a	1.a	$1$	$7$	$7$	$11.859$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		201.4.a.c	$1$	$1$	\(-1\)	\(-21\)	\(11\)	\(-33\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
201.4.a.d	$201$	$4$	201.a	1.a	$1$	$9$	$9$	$11.859$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	201.4.a.d	$1$	$0$	\(3\)	\(-27\)	\(12\)	\(8\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
201.4.a.e	$201$	$4$	201.a	1.a	$1$	$11$	$11$	$11.859$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	201.4.a.e	$1$	$0$	\(3\)	\(33\)	\(8\)	\(78\)		$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(201))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(201)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)