Space of modular forms of level 102, weight 2, and trivial character

• Label: 102.2.a
• Level: $102$
• Weight: $2$
• Character orbit: 102.a
• Rep. character: $\chi_{102}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	102.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(102))\).

	Total	New	Old
Modular forms	22	3	19
Cusp forms	15	3	12
Eisenstein series	7	0	7

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

\(2\)	\(3\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(10\)	\(1\)	\(9\)		\(7\)	\(1\)	\(6\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(12\)	\(2\)	\(10\)		\(8\)	\(2\)	\(6\)		\(4\)	\(0\)	\(4\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(102))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	17
102.2.a.a	$102$	$2$	102.a	1.a	$1$	$1$	$1$	$0.814$	\(\Q\)	None	✓	✓	✓	✓	102.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
102.2.a.b	$102$	$2$	102.a	1.a	$1$	$1$	$1$	$0.814$	\(\Q\)	None	✓	✓	✓	✓	102.2.a.b	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
102.2.a.c	$102$	$2$	102.a	1.a	$1$	$1$	$1$	$0.814$	\(\Q\)	None	✓	✓	✓	✓	102.2.a.c	$1$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(102)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)