Space of modular forms of level 3420, weight 2, and Character 3420.bj

• Label: 3420.2.bj
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.bj
• Rep. character: $\chi_{3420}(1189,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $100$
• Newform subspaces: $5$
• Sturm bound: $1440$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1440\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3420, [\chi])\).

	Total	New	Old
Modular forms	1488	100	1388
Cusp forms	1392	100	1292
Eisenstein series	96	0	96

Trace form

\( 100 q + q^{5} - 10 q^{19} - 3 q^{25} + 8 q^{29} - 8 q^{31} + 4 q^{35} - 22 q^{41} - 92 q^{49} + 44 q^{59} - 6 q^{61} + 14 q^{65} - 14 q^{71} + 9 q^{85} + 8 q^{89} + 28 q^{91} + 17 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3420, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3420.2.bj.a	$3420$	$2$	3420.bj	95.i	$6$	$4$	$2$	$27.309$	\(\Q(\zeta_{12})\)	None					1140.2.bg.b	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{3}-\beta_{2}-\beta_1)q^{5}-5 q^{11}-\beta_1 q^{13}+\cdots\)
3420.2.bj.b	$3420$	$2$	3420.bj	95.i	$6$	$4$	$2$	$27.309$	\(\Q(\zeta_{12})\)	None					1140.2.bg.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+4q^{11}+\cdots\)
3420.2.bj.c	$3420$	$2$	3420.bj	95.i	$6$	$20$	$10$	$27.309$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					380.2.r.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{5}+(-\beta _{15}+\beta _{18})q^{7}+\beta _{6}q^{11}+\cdots\)
3420.2.bj.d	$3420$	$2$	3420.bj	95.i	$6$	$32$	$16$	$27.309$		None					1140.2.bg.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
3420.2.bj.e	$3420$	$2$	3420.bj	95.i	$6$	$40$	$20$	$27.309$		None		✓	✓		3420.2.bj.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1710, [\chi])\)\(^{\oplus 2}\)