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

• Label: 3420.2.bb
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.bb
• Rep. character: $\chi_{3420}(37,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $6$
• Sturm bound: $1440$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bb (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1440\)
Trace bound:			\(11\)
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

\( 100 q + 2 q^{5} - 2 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3420.2.bb.a	$3420$	$2$	3420.bb	95.g	$4$	$8$	$4$	$27.309$	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{5}+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
3420.2.bb.b	$3420$	$2$	3420.bb	95.g	$4$	$8$	$4$	$27.309$	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{1}q^{5}+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
3420.2.bb.c	$3420$	$2$	3420.bb	95.g	$4$	$8$	$4$	$27.309$	8.0.2702336256.1	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(2\)	\(-6\)	$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{2}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)
3420.2.bb.d	$3420$	$2$	3420.bb	95.g	$4$	$12$	$6$	$27.309$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{6}-\beta _{8})q^{5}+\beta _{3}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
3420.2.bb.e	$3420$	$2$	3420.bb	95.g	$4$	$24$	$12$	$27.309$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{4}]$
3420.2.bb.f	$3420$	$2$	3420.bb	95.g	$4$	$40$	$20$	$27.309$		None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

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

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