Space of modular forms of level 130, weight 2, and Character 130.l

• Label: 130.2.l
• Level: $130$
• Weight: $2$
• Character orbit: 130.l
• Rep. character: $\chi_{130}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $42$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(130, [\chi])\).

	Total	New	Old
Modular forms	52	12	40
Cusp forms	36	12	24
Eisenstein series	16	0	16

Trace form

12 * q + 6 * q^4 - 6 * q^9 + 2 * q^10 - 6 * q^11 + 12 * q^13 - 12 * q^14 + 12 * q^15 - 6 * q^16 - 18 * q^19 - 12 * q^25 + 24 * q^27 + 12 * q^29 + 4 * q^30 - 60 * q^33 - 6 * q^35 + 6 * q^36 - 12 * q^37 - 24 * q^38 - 36 * q^39 + 4 * q^40 - 24 * q^41 - 12 * q^42 + 12 * q^46 + 12 * q^49 + 24 * q^51 + 48 * q^53 + 36 * q^54 + 12 * q^55 - 6 * q^56 + 12 * q^58 + 12 * q^59 + 24 * q^61 + 24 * q^62 + 48 * q^63 - 12 * q^64 + 6 * q^65 - 24 * q^66 + 24 * q^67 + 12 * q^69 + 24 * q^72 + 18 * q^74 - 18 * q^76 - 24 * q^77 + 12 * q^78 + 24 * q^79 - 30 * q^81 + 12 * q^84 - 36 * q^85 + 24 * q^87 - 42 * q^89 - 4 * q^90 - 66 * q^91 + 36 * q^93 + 6 * q^94 + 36 * q^97 - 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
130.2.l.a	$130$	$2$	130.l	13.e	$6$	$4$	$2$	$1.038$	\(\Q(\zeta_{12})\)	None		✓			130.2.l.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
130.2.l.b	$130$	$2$	130.l	13.e	$6$	$8$	$4$	$1.038$	8.0.22581504.2	None		✓	✓		130.2.l.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(130, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(130, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)