Space of modular forms of level 2548, weight 2, and Character 2548.j

• Label: 2548.2.j
• Level: $2548$
• Weight: $2$
• Character orbit: 2548.j
• Rep. character: $\chi_{2548}(1145,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $19$
• Sturm bound: $784$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(784\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2548, [\chi])\).

	Total	New	Old
Modular forms	832	80	752
Cusp forms	736	80	656
Eisenstein series	96	0	96

Trace form

\( 80 q - 6 q^{5} - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2548, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2548.2.j.a	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}-3\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
2548.2.j.b	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}+(3-3\zeta_{6})q^{11}+\cdots\)
2548.2.j.c	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2548.2.j.d	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.e	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.f	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.g	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.h	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
2548.2.j.i	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
2548.2.j.j	$2548$	$2$	2548.j	7.c	$3$	$2$	$1$	$20.346$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2548.2.j.k	$2548$	$2$	2548.j	7.c	$3$	$4$	$2$	$20.346$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
2548.2.j.l	$2548$	$2$	2548.j	7.c	$3$	$4$	$2$	$20.346$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2548.2.j.m	$2548$	$2$	2548.j	7.c	$3$	$4$	$2$	$20.346$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-3+\cdots)q^{9}+\cdots\)
2548.2.j.n	$2548$	$2$	2548.j	7.c	$3$	$4$	$2$	$20.346$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
2548.2.j.o	$2548$	$2$	2548.j	7.c	$3$	$6$	$3$	$20.346$	6.0.1714608.1	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}+\beta _{5})q^{3}+(-\beta _{1}+\beta _{4}+\beta _{5})q^{5}+\cdots\)
2548.2.j.p	$2548$	$2$	2548.j	7.c	$3$	$6$	$3$	$20.346$	6.0.1714608.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{1}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
2548.2.j.q	$2548$	$2$	2548.j	7.c	$3$	$8$	$4$	$20.346$	8.0.856615824.2	None		$2$	$0$	\(0\)	\(3\)	\(-1\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{4})q^{3}-\beta _{6}q^{5}+(-3+3\beta _{1}+\cdots)q^{9}+\cdots\)
2548.2.j.r	$2548$	$2$	2548.j	7.c	$3$	$12$	$6$	$20.346$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2}+\beta _{7})q^{3}+(-2+2\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots\)
2548.2.j.s	$2548$	$2$	2548.j	7.c	$3$	$12$	$6$	$20.346$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{7})q^{3}+(2-2\beta _{6}+\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2548, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2548, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)