Properties

Label 1008.2.r
Level $1008$
Weight $2$
Character orbit 1008.r
Rep. character $\chi_{1008}(337,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $14$
Sturm bound $384$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 408 72 336
Cusp forms 360 72 288
Eisenstein series 48 0 48

Trace form

\( 72 q + 4 q^{9} + O(q^{10}) \) \( 72 q + 4 q^{9} - 12 q^{11} - 12 q^{15} + 8 q^{17} + 12 q^{23} - 36 q^{25} + 36 q^{27} + 12 q^{33} + 24 q^{35} + 36 q^{39} + 4 q^{41} + 12 q^{47} - 36 q^{49} - 12 q^{51} - 4 q^{57} - 12 q^{59} - 8 q^{65} - 80 q^{71} + 24 q^{73} - 68 q^{75} - 20 q^{81} + 4 q^{87} - 16 q^{89} - 24 q^{93} + 32 q^{95} - 12 q^{97} + 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.2.r.a 1008.r 9.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 126.2.f.b \(0\) \(-3\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1008.2.r.b 1008.r 9.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 504.2.r.b \(0\) \(-3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1008.2.r.c 1008.r 9.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 504.2.r.a \(0\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1008.2.r.d 1008.r 9.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 126.2.f.a \(0\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1008.2.r.e 1008.r 9.c $4$ $8.049$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 126.2.f.c \(0\) \(-4\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1008.2.r.f 1008.r 9.c $4$ $8.049$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 126.2.f.d \(0\) \(1\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{3})q^{3}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots\)
1008.2.r.g 1008.r 9.c $6$ $8.049$ 6.0.309123.1 None 252.2.j.b \(0\) \(-2\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1008.2.r.h 1008.r 9.c $6$ $8.049$ \(\Q(\zeta_{18})\) None 63.2.f.a \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{3}+(-1+\zeta_{18}+\zeta_{18}^{5})q^{5}+\cdots\)
1008.2.r.i 1008.r 9.c $6$ $8.049$ \(\Q(\zeta_{18})\) None 504.2.r.c \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}^{4}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
1008.2.r.j 1008.r 9.c $6$ $8.049$ 6.0.309123.1 None 252.2.j.a \(0\) \(2\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
1008.2.r.k 1008.r 9.c $6$ $8.049$ 6.0.309123.1 None 63.2.f.b \(0\) \(4\) \(5\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{5})q^{3}+(2+\beta _{2}+2\beta _{4}-\beta _{5})q^{5}+\cdots\)
1008.2.r.l 1008.r 9.c $8$ $8.049$ 8.0.2091141441.1 None 504.2.r.e \(0\) \(1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{6})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1008.2.r.m 1008.r 9.c $8$ $8.049$ 8.0.508277025.1 None 504.2.r.d \(0\) \(4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}+(\beta _{2}-\beta _{3}+\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots\)
1008.2.r.n 1008.r 9.c $10$ $8.049$ 10.0.\(\cdots\).1 None 504.2.r.f \(0\) \(0\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)