Space of modular forms of level 6468, weight 2, and trivial character

• Label: 6468.2.a
• Level: $6468$
• Weight: $2$
• Character orbit: 6468.a
• Rep. character: $\chi_{6468}(1,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $32$
• Sturm bound: $2688$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 6468 = 2^{2} \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6468.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 32 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6468))\).

	Total	New	Old
Modular forms	1392	70	1322
Cusp forms	1297	70	1227
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(9\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(11\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(6\)
Plus space				\(+\)	\(30\)
Minus space				\(-\)	\(40\)

Trace form

\( 70 q + 4 q^{5} + 70 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6468))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	11
6468.2.a.a	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{9}-q^{11}+q^{13}+3q^{15}+\cdots\)
6468.2.a.b	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+q^{11}+2q^{13}+\cdots\)
6468.2.a.c	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+q^{11}+2q^{13}+\cdots\)
6468.2.a.d	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+q^{11}+7q^{13}+q^{15}+\cdots\)
6468.2.a.e	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-q^{11}-3q^{13}+2q^{17}+\cdots\)
6468.2.a.f	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{13}-q^{15}+\cdots\)
6468.2.a.g	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+q^{11}+2q^{13}+\cdots\)
6468.2.a.h	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
6468.2.a.i	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}+q^{11}-q^{13}-3q^{15}+\cdots\)
6468.2.a.j	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}+q^{11}+7q^{13}+\cdots\)
6468.2.a.k	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{9}+q^{11}+q^{13}-3q^{15}+\cdots\)
6468.2.a.l	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-q^{11}-6q^{13}+\cdots\)
6468.2.a.m	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+q^{11}-2q^{13}+\cdots\)
6468.2.a.n	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+q^{11}+q^{13}-q^{15}+\cdots\)
6468.2.a.o	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-q^{11}+3q^{13}-2q^{17}+\cdots\)
6468.2.a.p	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+q^{15}+\cdots\)
6468.2.a.q	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+q^{11}-7q^{13}+q^{15}+\cdots\)
6468.2.a.r	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+q^{11}+q^{13}+q^{15}+\cdots\)
6468.2.a.s	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+q^{11}-2q^{13}+\cdots\)
6468.2.a.t	$6468$	$2$	6468.a	1.a	$1$	$1$	$1$	$51.647$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{9}-q^{11}-q^{13}+3q^{15}+\cdots\)
6468.2.a.u	$6468$	$2$	6468.a	1.a	$1$	$2$	$2$	$51.647$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
6468.2.a.v	$6468$	$2$	6468.a	1.a	$1$	$2$	$2$	$51.647$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-q^{11}+4q^{13}+(-3+\beta )q^{17}+\cdots\)
6468.2.a.w	$6468$	$2$	6468.a	1.a	$1$	$2$	$2$	$51.647$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-q^{11}-4q^{13}+(3-\beta )q^{17}+\cdots\)
6468.2.a.x	$6468$	$2$	6468.a	1.a	$1$	$2$	$2$	$51.647$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+q^{9}-q^{11}+3q^{13}+\cdots\)
6468.2.a.y	$6468$	$2$	6468.a	1.a	$1$	$4$	$4$	$51.647$	4.4.96336.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{9}-q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots\)
6468.2.a.z	$6468$	$2$	6468.a	1.a	$1$	$4$	$4$	$51.647$	4.4.96336.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+q^{9}-q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots\)
6468.2.a.ba	$6468$	$2$	6468.a	1.a	$1$	$5$	$5$	$51.647$	5.5.81384912.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+q^{9}+q^{11}+(\beta _{2}-\beta _{4})q^{13}+\cdots\)
6468.2.a.bb	$6468$	$2$	6468.a	1.a	$1$	$5$	$5$	$51.647$	5.5.81384912.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+q^{9}+q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
6468.2.a.bc	$6468$	$2$	6468.a	1.a	$1$	$6$	$6$	$51.647$	6.6.152932864.1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+q^{9}+q^{11}+\cdots\)
6468.2.a.bd	$6468$	$2$	6468.a	1.a	$1$	$6$	$6$	$51.647$	6.6.126956032.1	None	✓	$1$	$0$	\(0\)	\(-6\)	\(4\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{3})q^{5}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
6468.2.a.be	$6468$	$2$	6468.a	1.a	$1$	$6$	$6$	$51.647$	6.6.126956032.1	None	✓	$1$	$1$	\(0\)	\(6\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}-q^{11}+\cdots\)
6468.2.a.bf	$6468$	$2$	6468.a	1.a	$1$	$6$	$6$	$51.647$	6.6.152932864.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(4\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+q^{9}+q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\)\(^{\oplus 2}\)