Space of Modular Forms of Level 1008, Weight 2, and Character 1008.b

• Label: 1008.2.b
• Level: 1008
• Weight: 2
• Character orbit: b
• Rep. character: \(\chi_{1008}(559,\cdot)\)
• Character field: \(\Q\)
• Dimension: 20
• Newforms: 9
• Sturm bound: 384
• Trace bound: 19

Defining parameters

Level:	\( N \)	=	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	1008.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 28 \)
Character field:			\(\Q\)
Newforms:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

	Total	New	Old
Modular forms	216	20	196
Cusp forms	168	20	148
Eisenstein series	48	0	48

Trace form

\(20q \) \(\mathstrut +\mathstrut O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into irreducible Hecke orbits

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)
1008.2.b.a	\(2\)	\(8.049\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(q+(-2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}-4\zeta_{6}q^{17}+\cdots\)
1008.2.b.b	\(2\)	\(8.049\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(q-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
1008.2.b.c	\(2\)	\(8.049\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(-4\)	\(q+(-2+\zeta_{6})q^{7}-4\zeta_{6}q^{13}+8q^{19}+\cdots\)
1008.2.b.d	\(2\)	\(8.049\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(q+\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.e	\(2\)	\(8.049\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(q+\beta q^{5}+(1+\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.f	\(2\)	\(8.049\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(4\)	\(q+(2-\zeta_{6})q^{7}-4\zeta_{6}q^{13}-8q^{19}+5q^{25}+\cdots\)
1008.2.b.g	\(2\)	\(8.049\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)	\(q-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
1008.2.b.h	\(2\)	\(8.049\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(4\)	\(q+(2+\zeta_{6})q^{7}-2\zeta_{6}q^{11}+4\zeta_{6}q^{17}+\cdots\)
1008.2.b.i	\(4\)	\(8.049\)	\(\Q(\sqrt{-6}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+3\beta _{1}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)