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

• Label: 364.2.v
• Level: $364$
• Weight: $2$
• Character orbit: 364.v
• Rep. character: $\chi_{364}(55,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $104$
• Newform subspaces: $6$
• Sturm bound: $112$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	364.v (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 364 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(112\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

104 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 48 * q^9 - 16 * q^14 + 6 * q^16 + 12 * q^18 - 4 * q^21 - 22 * q^22 - 88 * q^25 - 8 * q^28 - 4 * q^29 + 12 * q^30 + 18 * q^32 - 12 * q^36 - 20 * q^37 + 32 * q^42 - 8 * q^44 - 18 * q^49 - 14 * q^50 - 32 * q^53 + 22 * q^56 + 120 * q^57 + 18 * q^58 + 132 * q^60 - 80 * q^64 + 48 * q^65 + 36 * q^70 + 22 * q^72 + 20 * q^74 - 60 * q^77 - 142 * q^78 - 28 * q^81 - 62 * q^84 + 16 * q^85 + 88 * q^86 + 26 * q^88 - 144 * q^92 - 8 * q^93 - 20 * q^98

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.v.a	$364$	$2$	364.v	364.v	$6$	$4$	$2$	$2.907$	\(\Q(\zeta_{12})\)	None		✓			364.2.v.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
364.2.v.b	$364$	$2$	364.v	364.v	$6$	$4$	$2$	$2.907$	\(\Q(\zeta_{12})\)	None		✓			364.2.v.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
364.2.v.c	$364$	$2$	364.v	364.v	$6$	$8$	$4$	$2.907$	8.0.592240896.1	None		✓			364.2.v.c	$4$	$0$	\(-4\)	\(-6\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{3})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\cdots\)
364.2.v.d	$364$	$2$	364.v	364.v	$6$	$8$	$4$	$2.907$	8.0.592240896.1	None		✓			364.2.v.c	$4$	$0$	\(-4\)	\(6\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{2}+\beta _{3}+\beta _{7})q^{2}+(1-2\beta _{3}+\cdots)q^{3}+\cdots\)
364.2.v.e	$364$	$2$	364.v	364.v	$6$	$8$	$4$	$2.907$	8.0.49787136.1	None		✓			364.2.v.e	$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+(\beta _{3}-2\beta _{7})q^{3}+\cdots\)
364.2.v.f	$364$	$2$	364.v	364.v	$6$	$72$	$36$	$2.907$		None		✓	✓		364.2.v.f	$8$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$