Space of modular forms of level 9, weight 102, and trivial character

• Label: 9.102.a
• Level: $9$
• Weight: $102$
• Character orbit: 9.a
• Rep. character: $\chi_{9}(1,\cdot)$
• Character field: $\Q$
• Dimension: $41$
• Newform subspaces: $4$
• Sturm bound: $102$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 102 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(102\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{102}(\Gamma_0(9))\).

	Total	New	Old
Modular forms	103	42	61
Cusp forms	99	41	58
Eisenstein series	4	1	3

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

\(3\)	Dim
\(+\)	\(16\)
\(-\)	\(25\)

Trace form

\( 41 q + 690910815047586 q^{2} + 53153830531493207222729237070356 q^{4} + 317752456970579700895898157312317994 q^{5} + 367735172587778874913291247197771445712280 q^{7} + 8239480627916718887748231785739053938667942232 q^{8} + O(q^{10}) \)

Decomposition of \(S_{102}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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
9.102.a.a	$9$	$102$	9.a	1.a	$1$	$8$	$8$	$581.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(-49\!\cdots\!16\)	\(0\)	\(19\!\cdots\!20\)	\(55\!\cdots\!92\)		$-$	$-$	$2^{97}\cdot 3^{56}\cdot 5^{11}\cdot 7^{8}\cdot 11^{2}\cdot 13^{2}\cdot 17^{3}$	$\mathrm{SU}(2)$	\(q+(-61420161900065-\beta _{1})q^{2}+\cdots\)
9.102.a.b	$9$	$102$	9.a	1.a	$1$	$8$	$8$	$581.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(43\!\cdots\!40\)	\(0\)	\(-38\!\cdots\!00\)	\(-57\!\cdots\!00\)		$-$	$-$	$2^{119}\cdot 3^{56}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}$	$\mathrm{SU}(2)$	\(q+(54373636474380+\beta _{1})q^{2}+\cdots\)
9.102.a.c	$9$	$102$	9.a	1.a	$1$	$9$	$9$	$581.406$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(74\!\cdots\!62\)	\(0\)	\(15\!\cdots\!74\)	\(-45\!\cdots\!52\)		$-$	$-$	$2^{120}\cdot 3^{73}\cdot 5^{14}\cdot 7^{8}\cdot 11^{3}\cdot 13\cdot 17^{2}$	$\mathrm{SU}(2)$	\(q+(83031446494785+\beta _{1})q^{2}+\cdots\)
9.102.a.d	$9$	$102$	9.a	1.a	$1$	$16$	$16$	$581.406$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(10\!\cdots\!40\)		$+$	$+$	$2^{242}\cdot 3^{256}\cdot 5^{36}\cdot 7^{16}\cdot 11^{4}\cdot 13^{4}\cdot 17^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1422135952984546363578721149778+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{102}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces

\( S_{102}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{102}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{102}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)