Space of modular forms of level 10427, weight 2, and trivial character

• Label: 10427.2.a
• Level: $10427$
• Weight: $2$
• Character orbit: 10427.a
• Rep. character: $\chi_{10427}(1,\cdot)$
• Character field: $\Q$
• Dimension: $869$
• Newform subspaces: $3$
• Sturm bound: $1738$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 10427 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	10427.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1738\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(10427))\).

	Total	New	Old
Modular forms	870	870	0
Cusp forms	869	869	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.

\(10427\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(404\)	\(404\)	\(0\)		\(404\)	\(404\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(466\)	\(466\)	\(0\)		\(465\)	\(465\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

869 * q - 2 * q^2 + 866 * q^4 + 2 * q^5 - 12 * q^6 - 6 * q^8 + 867 * q^9 + 4 * q^10 + 2 * q^11 + 4 * q^12 + 6 * q^13 + 4 * q^14 + 4 * q^15 + 856 * q^16 + 4 * q^17 - 2 * q^18 + 14 * q^20 - 4 * q^21 - 2 * q^22 + 2 * q^23 - 24 * q^24 + 865 * q^25 - 12 * q^26 - 6 * q^27 + 16 * q^28 - 2 * q^29 + 10 * q^30 + 8 * q^31 + 6 * q^32 - 14 * q^33 + 4 * q^34 + 20 * q^35 + 860 * q^36 + 16 * q^37 + 18 * q^38 + 10 * q^39 - 4 * q^40 + 2 * q^41 + 14 * q^43 - 16 * q^44 + 8 * q^45 - 18 * q^46 + 60 * q^48 + 881 * q^49 + 8 * q^50 - 18 * q^51 - 6 * q^52 + 10 * q^53 - 22 * q^54 + 4 * q^55 + 6 * q^56 - 18 * q^57 - 20 * q^58 - 22 * q^59 + 12 * q^60 + 14 * q^61 - 24 * q^62 + 10 * q^63 + 834 * q^64 + 38 * q^65 - 6 * q^66 - 14 * q^67 + 28 * q^68 - 44 * q^69 - 54 * q^70 + 18 * q^72 + 18 * q^73 - 6 * q^74 + 18 * q^75 + 26 * q^76 - 14 * q^77 + 30 * q^78 - 10 * q^79 + 821 * q^81 + 28 * q^82 + 38 * q^83 + 42 * q^84 + 20 * q^85 - 24 * q^86 - 8 * q^87 - 40 * q^88 + 2 * q^89 - 42 * q^90 + 40 * q^91 + 6 * q^92 - 8 * q^93 - 28 * q^94 + 8 * q^95 - 106 * q^96 + 22 * q^97 - 26 * q^98 - 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(10427))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		10427
10427.2.a.a	$10427$	$2$	10427.a	1.a	$1$	$1$	$1$	$83.260$	\(\Q\)	None	✓	✓			10427.2.a.a	$1$		\(-2\)	\(-1\)	\(0\)	\(-2\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-2q^{7}+\cdots\)
10427.2.a.b	$10427$	$2$	10427.a	1.a	$1$	$404$	$404$	$83.260$		None	✓	✓	✓	✓	10427.2.a.b	$1$		\(-13\)	\(-49\)	\(-75\)	\(-88\)		$+$	$+$		$\mathrm{SU}(2)$
10427.2.a.c	$10427$	$2$	10427.a	1.a	$1$	$464$	$464$	$83.260$		None	✓	✓	✓		10427.2.a.c	$1$		\(13\)	\(50\)	\(77\)	\(90\)		$-$	$-$		$\mathrm{SU}(2)$