Space of modular forms of level 468, weight 2, and trivial character

• Label: 468.2.a
• Level: $468$
• Weight: $2$
• Character orbit: 468.a
• Rep. character: $\chi_{468}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $5$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(168\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(468))\).

	Total	New	Old
Modular forms	96	5	91
Cusp forms	73	5	68
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.

\(2\)	\(3\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(11\)	\(0\)	\(11\)		\(8\)	\(0\)	\(8\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(13\)	\(0\)	\(13\)		\(9\)	\(0\)	\(9\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(14\)	\(0\)	\(14\)		\(10\)	\(0\)	\(10\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(12\)	\(0\)	\(12\)		\(8\)	\(0\)	\(8\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(13\)	\(2\)	\(11\)		\(11\)	\(2\)	\(9\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)		\(11\)	\(0\)	\(11\)		\(9\)	\(0\)	\(9\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)		\(10\)	\(1\)	\(9\)		\(8\)	\(1\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)		\(12\)	\(2\)	\(10\)		\(10\)	\(2\)	\(8\)		\(2\)	\(0\)	\(2\)
Plus space			\(+\)		\(44\)	\(1\)	\(43\)		\(33\)	\(1\)	\(32\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(52\)	\(4\)	\(48\)		\(40\)	\(4\)	\(36\)		\(12\)	\(0\)	\(12\)

Trace form

5 * q + 2 * q^5 + 6 * q^7 + 6 * q^11 - q^13 - 2 * q^17 - 6 * q^19 - 8 * q^23 + 27 * q^25 + 10 * q^29 + 10 * q^31 - 4 * q^35 + 18 * q^37 + 10 * q^41 - 12 * q^43 + 6 * q^47 + 9 * q^49 - 2 * q^53 - 20 * q^55 + 6 * q^59 - 18 * q^61 + 6 * q^65 - 14 * q^67 - 38 * q^71 - 14 * q^73 - 12 * q^77 - 20 * q^79 - 6 * q^83 + 4 * q^85 + 10 * q^89 - 6 * q^91 + 4 * q^95 + 18 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(468))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	13
468.2.a.a	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	\(\Q\)	None	✓	✓			468.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots\)
468.2.a.b	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	\(\Q\)	None	✓		✓	✓	52.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\)
468.2.a.c	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	\(\Q\)	None	✓				156.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
468.2.a.d	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	\(\Q\)	None	✓				156.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\)
468.2.a.e	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	\(\Q\)	None	✓	✓			468.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(468)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)