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Properties

Label 1008.2.s
Level $1008$
Weight $2$
Character orbit 1008.s
Rep. character $\chi_{1008}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $38$
Newform subspaces $18$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 18 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

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

Total New Old
Modular forms 432 42 390
Cusp forms 336 38 298
Eisenstein series 96 4 92

Trace form

\( 38 q + q^{5} + O(q^{10}) \) \( 38 q + q^{5} - 3 q^{11} - 4 q^{13} + q^{17} + 9 q^{19} - 9 q^{23} - 20 q^{25} + 4 q^{29} - 9 q^{31} - 15 q^{35} + 3 q^{37} - 4 q^{41} + 16 q^{43} + 15 q^{47} + 6 q^{49} + 9 q^{53} + 22 q^{55} - 11 q^{59} + 3 q^{61} + 18 q^{65} + 7 q^{67} + 8 q^{71} + 11 q^{73} - 25 q^{77} + 13 q^{79} + 64 q^{83} - 10 q^{85} - 3 q^{89} + 52 q^{91} + 45 q^{95} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.2.s.a 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-3q^{13}+\cdots\)
1008.2.s.b 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1008.2.s.c 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1008.2.s.d 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
1008.2.s.e 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
1008.2.s.f 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1008.2.s.g 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1008.2.s.h 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
1008.2.s.i 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{3}]$ \(q+(-2-\zeta_{6})q^{7}+5q^{13}-\zeta_{6}q^{19}+\cdots\)
1008.2.s.j 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-3\zeta_{6})q^{7}-7q^{13}-7\zeta_{6}q^{19}+\cdots\)
1008.2.s.k 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
1008.2.s.l 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
1008.2.s.m 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1008.2.s.n 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1008.2.s.o 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1008.2.s.p 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1008.2.s.q 1008.s 7.c $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-3q^{13}+\cdots\)
1008.2.s.r 1008.s 7.c $4$ $8.049$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-1\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\beta _{1}-\beta _{3})q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)