Space of modular forms of level 1716, weight 2, and trivial character

• Label: 1716.2.a
• Level: $1716$
• Weight: $2$
• Character orbit: 1716.a
• Rep. character: $\chi_{1716}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $9$
• Sturm bound: $672$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(672\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1716))\).

	Total	New	Old
Modular forms	348	20	328
Cusp forms	325	20	305
Eisenstein series	23	0	23

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

\(2\)	\(3\)	\(11\)	\(13\)	Fricke	Dim.
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
Plus space				\(+\)	\(6\)
Minus space				\(-\)	\(14\)

Trace form

\( 20q + 20q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\) into newform subspaces

Label	Dim.	\(A\)	Field	CM	Traces					A-L signs				$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)		2	3	11	13
1716.2.a.a	\(1\)	\(13.702\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)		\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{7}+q^{9}-q^{11}+q^{13}-2q^{17}+\cdots\)
1716.2.a.b	\(1\)	\(13.702\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(-2\)		\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1716.2.a.c	\(1\)	\(13.702\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)		\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+2q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots\)
1716.2.a.d	\(2\)	\(13.702\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(-2\)	\(0\)		\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+(-1+\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots\)
1716.2.a.e	\(2\)	\(13.702\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)		\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+(-2+\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots\)
1716.2.a.f	\(3\)	\(13.702\)	3.3.1620.1	None	\(0\)	\(-3\)	\(0\)	\(0\)		\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}-q^{11}+\cdots\)
1716.2.a.g	\(3\)	\(13.702\)	3.3.564.1	None	\(0\)	\(3\)	\(2\)	\(4\)		\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
1716.2.a.h	\(3\)	\(13.702\)	3.3.404.1	None	\(0\)	\(3\)	\(4\)	\(-4\)		\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
1716.2.a.i	\(4\)	\(13.702\)	4.4.90996.1	None	\(0\)	\(-4\)	\(2\)	\(2\)		\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1716))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1716)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 2}\)