Space of modular forms of level 1848, weight 2, and Character 1848.v

• Label: 1848.2.v
• Level: $1848$
• Weight: $2$
• Character orbit: 1848.v
• Rep. character: $\chi_{1848}(881,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $5$
• Sturm bound: $768$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1848.v (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(768\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

	Total	New	Old
Modular forms	400	80	320
Cusp forms	368	80	288
Eisenstein series	32	0	32

Trace form

\( 80 q + 4 q^{7} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1848.2.v.a	$1848$	$2$	1848.v	21.c	$2$	$8$	$8$	$14.756$	8.0.\(\cdots\).10	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
1848.2.v.b	$1848$	$2$	1848.v	21.c	$2$	$8$	$8$	$14.756$	8.0.342102016.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{5}-\beta _{6})q^{3}+\beta _{2}q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
1848.2.v.c	$1848$	$2$	1848.v	21.c	$2$	$16$	$16$	$14.756$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+(\beta _{6}+\beta _{9}-\beta _{12})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1848.2.v.d	$1848$	$2$	1848.v	21.c	$2$	$16$	$16$	$14.756$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}-\beta _{15})q^{3}+(\beta _{5}-\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots\)
1848.2.v.e	$1848$	$2$	1848.v	21.c	$2$	$32$	$32$	$14.756$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 2}\)