Space of modular forms of level 67, weight 4, and trivial character

• Label: 67.4.a
• Level: $67$
• Weight: $4$
• Character orbit: 67.a
• Rep. character: $\chi_{67}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	67.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(67))\).

	Total	New	Old
Modular forms	18	16	2
Cusp forms	16	16	0
Eisenstein series	2	0	2

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

\(67\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(10\)	\(9\)	\(1\)		\(9\)	\(9\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(8\)	\(7\)	\(1\)		\(7\)	\(7\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

16 * q + 2 * q^2 + 48 * q^4 - 30 * q^6 - 8 * q^7 + 30 * q^8 + 94 * q^9 - 12 * q^10 - 8 * q^11 - 56 * q^12 + 84 * q^13 - 202 * q^14 - 108 * q^15 + 260 * q^16 - 112 * q^17 - 20 * q^18 - 42 * q^19 - 138 * q^20 - 108 * q^21 + 196 * q^22 - 336 * q^23 + 204 * q^24 + 346 * q^25 + 264 * q^26 - 444 * q^27 - 270 * q^28 + 66 * q^29 + 514 * q^30 + 440 * q^31 + 382 * q^32 - 420 * q^33 + 46 * q^34 + 468 * q^35 - 810 * q^36 - 418 * q^37 - 572 * q^38 + 52 * q^39 - 902 * q^40 - 112 * q^41 - 24 * q^42 - 744 * q^43 - 386 * q^44 + 564 * q^45 + 534 * q^46 + 220 * q^47 + 190 * q^48 + 924 * q^49 - 162 * q^50 + 1836 * q^51 - 134 * q^52 + 1100 * q^53 - 702 * q^54 - 172 * q^55 - 2398 * q^56 - 80 * q^57 - 602 * q^58 - 246 * q^59 + 394 * q^60 + 696 * q^61 + 1874 * q^62 - 404 * q^63 + 122 * q^64 + 1296 * q^65 - 1674 * q^66 - 134 * q^67 + 490 * q^68 - 1520 * q^69 + 3034 * q^70 + 386 * q^71 - 2282 * q^72 + 1932 * q^73 + 1844 * q^74 + 1052 * q^75 + 686 * q^76 - 2964 * q^77 + 900 * q^78 + 548 * q^79 + 784 * q^80 + 1224 * q^81 + 1576 * q^82 + 1008 * q^83 - 622 * q^84 - 752 * q^85 - 502 * q^86 - 152 * q^87 - 922 * q^88 + 1316 * q^89 - 3374 * q^90 - 2484 * q^91 - 3464 * q^92 - 4808 * q^93 - 2900 * q^94 + 1980 * q^95 + 2372 * q^96 - 2100 * q^97 + 4664 * q^98 + 1592 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(67))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		67
67.4.a.a	$67$	$4$	67.a	1.a	$1$	$7$	$7$	$3.953$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	67.4.a.a	$1$	$1$	\(-6\)	\(-9\)	\(-45\)	\(-32\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{4})q^{3}+\cdots\)
67.4.a.b	$67$	$4$	67.a	1.a	$1$	$9$	$9$	$3.953$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	67.4.a.b	$1$	$0$	\(8\)	\(9\)	\(45\)	\(24\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{7})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)