Space of modular forms of level 50329, weight 2, and trivial character

• Label: 50329.2.a
• Level: $50329$
• Weight: $2$
• Character orbit: 50329.a
• Rep. character: $\chi_{50329}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4193$
• Newform subspaces: $3$
• Sturm bound: $8388$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 50329 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50329.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(8388\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(50329))\).

	Total	New	Old
Modular forms	4194	4194	0
Cusp forms	4193	4193	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.

\(50329\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(2058\)	\(2058\)	\(0\)		\(2058\)	\(2058\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(2136\)	\(2136\)	\(0\)		\(2135\)	\(2135\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

4193 * q - q^2 - 4 * q^3 + 4189 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^7 - 3 * q^8 + 4185 * q^9 - 10 * q^10 - 2 * q^11 - 4 * q^12 - 10 * q^13 - 4 * q^14 - 6 * q^15 + 4185 * q^16 - 4 * q^17 + 9 * q^18 - 18 * q^19 - 18 * q^20 - 18 * q^21 + 18 * q^22 - 2 * q^23 - 12 * q^24 + 4171 * q^25 - 10 * q^26 - 10 * q^27 - 20 * q^28 - 2 * q^29 + 10 * q^30 - 22 * q^31 + 13 * q^32 - 32 * q^33 - 42 * q^34 - 18 * q^35 + 4175 * q^36 - 16 * q^37 + 14 * q^38 - 8 * q^39 - 22 * q^40 - 26 * q^41 + 18 * q^42 - 6 * q^43 - 22 * q^44 - 34 * q^45 + 2 * q^46 - 8 * q^47 - 36 * q^48 + 4153 * q^49 + 15 * q^50 + 10 * q^51 - 8 * q^52 - 18 * q^53 - 40 * q^54 - 34 * q^55 + 32 * q^56 + 6 * q^57 + 2 * q^58 + 2 * q^59 + 32 * q^60 - 32 * q^61 + 34 * q^62 - 18 * q^63 + 4191 * q^64 + 6 * q^65 - 26 * q^66 - 22 * q^67 + 8 * q^68 - 28 * q^69 - 32 * q^70 + 10 * q^71 - 13 * q^72 - 38 * q^73 + 22 * q^74 - 12 * q^75 - 92 * q^76 - 24 * q^77 + 8 * q^78 + 12 * q^79 + 20 * q^80 + 4145 * q^81 - 18 * q^82 + 6 * q^83 - 60 * q^84 - 28 * q^85 + 46 * q^86 - 10 * q^87 + 44 * q^88 - 58 * q^89 - 20 * q^90 - 44 * q^91 - 10 * q^92 - 30 * q^93 - 12 * q^94 + 6 * q^95 - 32 * q^96 - 76 * q^97 + 23 * q^98 - 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(50329))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		50329
50329.2.a.a	$50329$	$2$	50329.a	1.a	$1$	$1$	$1$	$401.879$	\(\Q\)	None	✓	✓			50329.2.a.a	$1$		\(-1\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}+3q^{8}+\cdots\)
50329.2.a.b	$50329$	$2$	50329.a	1.a	$1$	$2057$	$2057$	$401.879$		None	✓	✓	✓		50329.2.a.b	$1$		\(-98\)	\(-59\)	\(-83\)	\(-106\)		$+$	$+$		$\mathrm{SU}(2)$
50329.2.a.c	$50329$	$2$	50329.a	1.a	$1$	$2135$	$2135$	$401.879$		None	✓	✓	✓	✓	50329.2.a.c	$1$		\(98\)	\(56\)	\(80\)	\(100\)		$-$	$-$		$\mathrm{SU}(2)$