Space of modular forms of level 1728, weight 2, and Character 1728.z

• Label: 1728.2.z
• Level: $1728$
• Weight: $2$
• Character orbit: 1728.z
• Rep. character: $\chi_{1728}(143,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.z (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1728, [\chi])\).

	Total	New	Old
Modular forms	1248	104	1144
Cusp forms	1056	88	968
Eisenstein series	192	16	176

Trace form

88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1728, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1728.2.z.a	$1728$	$2$	1728.z	144.u	$12$	$88$	$22$	$13.798$		None			✓	✓	144.2.u.a	$4$	$0$	\(0\)	\(0\)	\(6\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1728, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)