Space of modular forms of level 99, weight 14, and trivial character

• Label: 99.14.a
• Level: $99$
• Weight: $14$
• Character orbit: 99.a
• Rep. character: $\chi_{99}(1,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $9$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(99))\).

	Total	New	Old
Modular forms	160	54	106
Cusp forms	152	54	98
Eisenstein series	8	0	8

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

\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(11\)
\(+\)	\(-\)	$-$	\(11\)
\(-\)	\(+\)	$-$	\(17\)
\(-\)	\(-\)	$+$	\(15\)
Plus space		\(+\)	\(26\)
Minus space		\(-\)	\(28\)

Trace form

\( 54 q - 64 q^{2} + 233836 q^{4} + 31493 q^{5} + 27662 q^{7} - 2891040 q^{8} + O(q^{10}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(99))\) 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	11
99.14.a.a	$99$	$14$	99.a	1.a	$1$	$1$	$1$	$106.159$	\(\Q\)	None	✓	$1$	$1$	\(-140\)	\(0\)	\(-48740\)	\(487486\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-140q^{2}+11408q^{4}-48740q^{5}+\cdots\)
99.14.a.b	$99$	$14$	99.a	1.a	$1$	$4$	$4$	$106.159$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-41\)	\(0\)	\(38422\)	\(41998\)		$-$	$-$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-10-\beta _{1})q^{2}+(5909+43\beta _{1}+5\beta _{3})q^{4}+\cdots\)
99.14.a.c	$99$	$14$	99.a	1.a	$1$	$4$	$4$	$106.159$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(11\)	\(0\)	\(83432\)	\(69652\)		$-$	$+$	$-$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(-1564+37\beta _{1}+5\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.d	$99$	$14$	99.a	1.a	$1$	$5$	$5$	$106.159$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(53\)	\(0\)	\(-10318\)	\(-667804\)		$-$	$-$	$+$	$2^{5}\cdot 3^{6}$	$\mathrm{SU}(2)$	\(q+(11-\beta _{1})q^{2}+(7020-11\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
99.14.a.e	$99$	$14$	99.a	1.a	$1$	$5$	$5$	$106.159$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(64\)	\(0\)	\(454\)	\(-313920\)		$-$	$-$	$+$	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(13+\beta _{1})q^{2}+(-477+21\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.f	$99$	$14$	99.a	1.a	$1$	$6$	$6$	$106.159$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(-11\)	\(0\)	\(20932\)	\(284152\)		$-$	$+$	$-$	$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(3061-10\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.g	$99$	$14$	99.a	1.a	$1$	$7$	$7$	$106.159$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-52689\)	\(-89386\)		$-$	$+$	$-$	$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(6727+6\beta _{1}+\beta _{2})q^{4}+(-7527+\cdots)q^{5}+\cdots\)
99.14.a.h	$99$	$14$	99.a	1.a	$1$	$11$	$11$	$106.159$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-64\)	\(0\)	\(-62500\)	\(107742\)		$+$	$+$	$+$	$2^{20}\cdot 3^{22}\cdot 11$	$\mathrm{SU}(2)$	\(q+(-6+\beta _{1})q^{2}+(4859-11\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.i	$99$	$14$	99.a	1.a	$1$	$11$	$11$	$106.159$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(64\)	\(0\)	\(62500\)	\(107742\)		$+$	$-$	$-$	$2^{20}\cdot 3^{22}\cdot 11$	$\mathrm{SU}(2)$	\(q+(6-\beta _{1})q^{2}+(4859-11\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(99))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(99)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)