Space of modular forms of level 364, weight 2, and Character 364.u

• Label: 364.2.u
• Level: $364$
• Weight: $2$
• Character orbit: 364.u
• Rep. character: $\chi_{364}(225,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	364.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(364, [\chi])\).

	Total	New	Old
Modular forms	124	16	108
Cusp forms	100	16	84
Eisenstein series	24	0	24

Trace form

16 * q - 14 * q^9 + 6 * q^11 + 10 * q^13 + 6 * q^15 + 2 * q^17 - 44 * q^25 - 12 * q^27 - 22 * q^29 + 42 * q^33 - 6 * q^35 + 12 * q^37 + 24 * q^39 + 36 * q^41 + 6 * q^43 - 30 * q^45 + 8 * q^49 - 4 * q^51 + 8 * q^53 + 2 * q^55 - 18 * q^59 + 4 * q^61 - 12 * q^63 - 30 * q^65 + 24 * q^67 - 52 * q^69 + 36 * q^71 - 10 * q^75 - 24 * q^77 + 8 * q^79 + 42 * q^85 + 26 * q^87 - 36 * q^89 - 2 * q^91 - 42 * q^93 - 30 * q^95 - 42 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(364, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
364.2.u.a	$364$	$2$	364.u	13.e	$6$	$16$	$8$	$2.907$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	364.2.u.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{14})q^{3}+(\beta _{2}+\beta _{12}-\beta _{13}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(364, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(364, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)