Space of modular forms of level 100447, weight 2, and trivial character

• Label: 100447.2.a
• Level: $100447$
• Weight: $2$
• Character orbit: 100447.a
• Rep. character: $\chi_{100447}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8370$
• Newform subspaces: $2$
• Sturm bound: $16741$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 100447 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100447.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16741\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(100447))\).

	Total	New	Old
Modular forms	8371	8371	0
Cusp forms	8370	8370	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.

\(100447\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(4133\)	\(4133\)	\(0\)		\(4133\)	\(4133\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(4238\)	\(4238\)	\(0\)		\(4237\)	\(4237\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

8370 * q - q^2 + 8369 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^7 - 9 * q^8 + 8372 * q^9 - 8 * q^10 + 2 * q^11 - 14 * q^12 + 2 * q^13 - 20 * q^14 - 2 * q^15 + 8355 * q^16 + 4 * q^17 - 15 * q^18 + 2 * q^19 - 2 * q^20 - 24 * q^21 - 16 * q^22 - 8 * q^23 - 28 * q^24 + 8374 * q^25 - 16 * q^26 - 6 * q^27 - 22 * q^28 - 4 * q^29 + 14 * q^30 + 4 * q^31 - 19 * q^32 - 6 * q^33 + 6 * q^34 - 14 * q^35 + 8381 * q^36 - 4 * q^37 + 12 * q^38 - 8 * q^39 - 12 * q^40 - 2 * q^41 + 14 * q^42 - 8 * q^43 - 14 * q^44 + 10 * q^45 + 2 * q^46 - 4 * q^47 - 18 * q^48 + 8344 * q^49 - 51 * q^50 + 30 * q^51 - 26 * q^52 - 8 * q^53 - 38 * q^54 - 12 * q^55 - 64 * q^56 - 42 * q^57 - 8 * q^58 - 16 * q^59 - 18 * q^60 + 10 * q^61 - 16 * q^62 - 68 * q^63 + 8327 * q^64 + 12 * q^65 - 100 * q^66 - 18 * q^67 - 30 * q^68 - 8 * q^69 - 44 * q^70 - 4 * q^71 - 67 * q^72 + 6 * q^73 + 2 * q^74 - 18 * q^75 - 10 * q^76 - 30 * q^77 - 2 * q^78 - 16 * q^79 - 22 * q^80 + 8330 * q^81 + 12 * q^82 - 48 * q^83 - 32 * q^84 + 88 * q^85 + 30 * q^86 - 8 * q^87 - 52 * q^88 + 6 * q^89 - 14 * q^90 - 72 * q^91 - 2 * q^92 + 6 * q^93 - 28 * q^94 - 46 * q^95 - 48 * q^96 + 10 * q^97 - 9 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(100447))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		100447
100447.2.a.a	$100447$	$2$	100447.a	1.a	$1$	$4133$	$4133$	$802.073$		None	✓	✓	✓	✓	100447.2.a.a	$1$		\(-83\)	\(-151\)	\(-326\)	\(-105\)		$+$	$+$		$\mathrm{SU}(2)$
100447.2.a.b	$100447$	$2$	100447.a	1.a	$1$	$4237$	$4237$	$802.073$		None	✓	✓	✓	✓	100447.2.a.b	$1$		\(82\)	\(151\)	\(328\)	\(99\)		$-$	$-$		$\mathrm{SU}(2)$