Space of modular forms of level 41, weight 4, and trivial character

• Label: 41.4.a
• Level: $41$
• Weight: $4$
• Character orbit: 41.a
• Rep. character: $\chi_{41}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	41.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(41))\).

	Total	New	Old
Modular forms	12	10	2
Cusp forms	10	10	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.

\(41\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(8\)	\(7\)	\(1\)		\(7\)	\(7\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

10 * q - 2 * q^2 - 4 * q^3 + 38 * q^4 - 2 * q^7 + 18 * q^8 + 90 * q^9 + 84 * q^10 - 4 * q^11 - 150 * q^12 - 30 * q^13 - 180 * q^14 + 52 * q^15 + 70 * q^16 - 40 * q^17 - 386 * q^18 - 4 * q^19 - 304 * q^20 + 156 * q^21 + 198 * q^22 + 256 * q^23 + 76 * q^24 - 34 * q^25 - 214 * q^26 - 88 * q^27 - 238 * q^28 + 14 * q^29 - 478 * q^30 + 232 * q^31 + 982 * q^32 + 208 * q^33 - 228 * q^34 - 112 * q^35 + 586 * q^36 + 604 * q^37 + 8 * q^38 + 340 * q^39 + 648 * q^40 - 164 * q^41 + 408 * q^42 + 164 * q^43 - 140 * q^44 - 1160 * q^45 + 196 * q^46 + 398 * q^47 - 2034 * q^48 + 1238 * q^49 - 850 * q^50 + 1112 * q^51 - 1150 * q^52 - 454 * q^53 + 1430 * q^54 + 8 * q^55 - 1576 * q^56 - 2816 * q^57 + 818 * q^58 - 964 * q^59 + 186 * q^60 - 376 * q^61 + 688 * q^62 + 1094 * q^63 + 134 * q^64 - 236 * q^65 - 88 * q^66 - 1016 * q^67 + 764 * q^68 - 3808 * q^69 + 2422 * q^70 - 750 * q^71 - 3898 * q^72 + 1920 * q^73 + 2020 * q^74 + 500 * q^75 + 4414 * q^76 - 812 * q^77 - 800 * q^78 + 130 * q^79 - 796 * q^80 + 2010 * q^81 - 164 * q^82 + 1504 * q^83 + 2392 * q^84 - 2504 * q^85 - 1908 * q^86 + 644 * q^87 + 5138 * q^88 - 3452 * q^89 + 5832 * q^90 + 516 * q^91 + 5676 * q^92 + 3248 * q^93 + 1246 * q^94 - 1600 * q^95 - 2856 * q^96 - 1688 * q^97 - 4994 * q^98 + 512 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(41))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		41
41.4.a.a	$41$	$4$	41.a	1.a	$1$	$3$	$3$	$2.419$	3.3.404.1	None	✓	✓	✓	✓	41.4.a.a	$1$	$1$	\(-3\)	\(-8\)	\(-10\)	\(-50\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-3-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
41.4.a.b	$41$	$4$	41.a	1.a	$1$	$7$	$7$	$2.419$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	41.4.a.b	$1$	$0$	\(1\)	\(4\)	\(10\)	\(48\)		$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6})q^{3}+(6+\beta _{1}+\cdots)q^{4}+\cdots\)