Space of modular forms of level 202, weight 2, and trivial character

• Label: 202.2.a
• Level: $202$
• Weight: $2$
• Character orbit: 202.a
• Rep. character: $\chi_{202}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $51$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 202 = 2 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	202.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(51\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(202))\).

	Total	New	Old
Modular forms	27	8	19
Cusp forms	24	8	16
Eisenstein series	3	0	3

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

\(2\)	\(101\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(4\)	\(3\)	\(1\)		\(4\)	\(3\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(9\)	\(1\)	\(8\)		\(8\)	\(1\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(6\)	\(4\)	\(2\)		\(5\)	\(4\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(8\)	\(0\)	\(8\)		\(7\)	\(0\)	\(7\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(12\)	\(3\)	\(9\)		\(11\)	\(3\)	\(8\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(15\)	\(5\)	\(10\)		\(13\)	\(5\)	\(8\)		\(2\)	\(0\)	\(2\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(202))\) 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	101
202.2.a.a	$202$	$2$	202.a	1.a	$1$	$1$	$1$	$1.613$	\(\Q\)	None	✓	✓	✓	✓	202.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
202.2.a.b	$202$	$2$	202.a	1.a	$1$	$3$	$3$	$1.613$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓	✓	202.2.a.b	$1$	$1$	\(-3\)	\(-3\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
202.2.a.c	$202$	$2$	202.a	1.a	$1$	$4$	$4$	$1.613$	4.4.10273.1	None	✓	✓	✓	✓	202.2.a.c	$1$	$0$	\(4\)	\(-1\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(202))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(202)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(101))\)\(^{\oplus 2}\)