Space of modular forms of level 207, weight 2, and trivial character

• Label: 207.2.a
• Level: $207$
• Weight: $2$
• Character orbit: 207.a
• Rep. character: $\chi_{207}(1,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(207))\).

	Total	New	Old
Modular forms	28	9	19
Cusp forms	21	9	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.

\(3\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(10\)	\(2\)	\(8\)		\(8\)	\(2\)	\(6\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(7\)	\(4\)	\(3\)		\(5\)	\(4\)	\(1\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(7\)	\(1\)	\(6\)		\(5\)	\(1\)	\(4\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(11\)	\(3\)	\(8\)		\(8\)	\(3\)	\(5\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(17\)	\(6\)	\(11\)		\(13\)	\(6\)	\(7\)		\(4\)	\(0\)	\(4\)

Trace form

9 * q + 8 * q^4 + 4 * q^5 - 6 * q^7 + 3 * q^8 - 4 * q^10 - 6 * q^11 + 8 * q^14 + 6 * q^16 + 10 * q^20 - 14 * q^22 - 3 * q^23 + 3 * q^25 - 11 * q^26 - 22 * q^28 + 4 * q^29 - 14 * q^32 + 18 * q^34 - 16 * q^35 - 4 * q^37 + 6 * q^38 - 4 * q^40 - 12 * q^43 - 28 * q^44 + 2 * q^46 + 8 * q^47 - 11 * q^49 - 4 * q^50 + 3 * q^52 + 26 * q^53 + 4 * q^55 + 14 * q^56 + 33 * q^58 + 6 * q^61 - 39 * q^62 - 43 * q^64 + 26 * q^65 + 26 * q^67 + 32 * q^68 - 12 * q^70 - 12 * q^71 + 12 * q^73 + 24 * q^74 - 26 * q^76 + 16 * q^77 + 4 * q^79 - 20 * q^80 + 15 * q^82 + 2 * q^83 + 44 * q^85 - 40 * q^86 - 18 * q^88 + 26 * q^89 - 2 * q^91 - 6 * q^92 + 3 * q^94 - 4 * q^95 - 20 * q^97 + 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(207))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	23
207.2.a.a	$207$	$2$	207.a	1.a	$1$	$1$	$1$	$1.653$	\(\Q\)	None	✓		✓	✓	69.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{7}+3q^{8}-4q^{11}+\cdots\)
207.2.a.b	$207$	$2$	207.a	1.a	$1$	$2$	$2$	$1.653$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	207.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-2-\beta )q^{5}+\cdots\)
207.2.a.c	$207$	$2$	207.a	1.a	$1$	$2$	$2$	$1.653$	\(\Q(\sqrt{5}) \)	None	✓				69.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}+(1+\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
207.2.a.d	$207$	$2$	207.a	1.a	$1$	$2$	$2$	$1.653$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(2-2\beta )q^{7}+\cdots\)
207.2.a.e	$207$	$2$	207.a	1.a	$1$	$2$	$2$	$1.653$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	207.2.a.b	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(207))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(207)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)