Space of modular forms of level 50423, weight 2, and trivial character

• Label: 50423.2.a
• Level: $50423$
• Weight: $2$
• Character orbit: 50423.a
• Rep. character: $\chi_{50423}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4202$
• Newform subspaces: $3$
• Sturm bound: $8404$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 50423 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50423.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(8404\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(50423))\).

	Total	New	Old
Modular forms	4203	4203	0
Cusp forms	4202	4202	0
Eisenstein series	1	1	0

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

\(50423\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(2004\)	\(2004\)	\(0\)		\(2004\)	\(2004\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(2199\)	\(2199\)	\(0\)		\(2198\)	\(2198\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

4202 * q - q^2 + 2 * q^3 + 4199 * q^4 - 2 * q^6 + 2 * q^7 + 3 * q^8 + 4206 * q^9 + 6 * q^10 + 16 * q^12 + 12 * q^13 - 4 * q^14 + 4 * q^15 + 4189 * q^16 + 12 * q^17 + 9 * q^18 - 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 4212 * q^25 + 4 * q^26 + 32 * q^27 - 18 * q^28 - 8 * q^29 - 22 * q^30 + 6 * q^31 - 15 * q^32 + 24 * q^33 - 26 * q^34 + 14 * q^35 + 4209 * q^36 + 12 * q^37 + 12 * q^38 + 12 * q^39 - 10 * q^40 - 2 * q^41 - 12 * q^42 + 10 * q^43 + 8 * q^44 - 14 * q^45 - 68 * q^46 + 18 * q^47 + 60 * q^48 + 4204 * q^49 + 9 * q^50 + 18 * q^51 + 26 * q^52 + 28 * q^53 + 10 * q^55 - 38 * q^56 - 20 * q^57 - 16 * q^58 + 6 * q^59 - 2 * q^60 - 10 * q^61 + 12 * q^62 + 32 * q^63 + 4137 * q^64 - 14 * q^65 - 22 * q^66 + 22 * q^67 + 12 * q^68 + 2 * q^69 - 32 * q^70 + 26 * q^71 + 47 * q^72 + 26 * q^73 - 50 * q^74 + 60 * q^75 - 20 * q^76 - 10 * q^77 + 6 * q^78 + 8 * q^79 + 18 * q^80 + 4194 * q^81 + 14 * q^82 - 8 * q^83 + 34 * q^84 - 12 * q^85 - 60 * q^86 + 46 * q^87 - 64 * q^88 - 10 * q^89 + 104 * q^90 - 14 * q^91 + 34 * q^93 - 36 * q^94 + 30 * q^95 + 30 * q^96 + 64 * q^97 + 47 * q^98 + 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(50423))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		50423
50423.2.a.a	$50423$	$2$	50423.a	1.a	$1$	$2$	$2$	$402.630$	\(\Q(\sqrt{5}) \)	None	✓	✓			50423.2.a.a	$1$		\(1\)	\(-1\)	\(1\)	\(-7\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(-1+\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
50423.2.a.b	$50423$	$2$	50423.a	1.a	$1$	$2002$	$2002$	$402.630$		None	✓	✓	✓		50423.2.a.b	$1$		\(-45\)	\(-114\)	\(-88\)	\(-132\)		$+$	$+$		$\mathrm{SU}(2)$
50423.2.a.c	$50423$	$2$	50423.a	1.a	$1$	$2198$	$2198$	$402.630$		None	✓	✓	✓	✓	50423.2.a.c	$1$		\(43\)	\(117\)	\(87\)	\(141\)		$-$	$-$		$\mathrm{SU}(2)$