Space of modular forms of level 369, weight 2, and Character 369.u

• Label: 369.2.u
• Level: $369$
• Weight: $2$
• Character orbit: 369.u
• Rep. character: $\chi_{369}(46,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $136$
• Newform subspaces: $3$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(369, [\chi])\).

	Total	New	Old
Modular forms	368	152	216
Cusp forms	304	136	168
Eisenstein series	64	16	48

Trace form

\( 136 q + 10 q^{2} + 28 q^{4} + 10 q^{5} - 8 q^{7} + 10 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(369, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
369.2.u.a	$369$	$2$	369.u	41.g	$20$	$24$	$3$	$2.946$		None		$2$	$0$	\(10\)	\(0\)	\(10\)	\(-8\)		$\mathrm{SU}(2)[C_{20}]$
369.2.u.b	$369$	$2$	369.u	41.g	$20$	$48$	$6$	$2.946$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
369.2.u.c	$369$	$2$	369.u	41.g	$20$	$64$	$8$	$2.946$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(369, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(369, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 2}\)