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Properties

Label 1008.2.q
Level $1008$
Weight $2$
Character orbit 1008.q
Rep. character $\chi_{1008}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $92$
Newform subspaces $12$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
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 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q + q^{3} + q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 92 q + q^{3} + q^{5} + q^{7} - q^{9} - q^{11} - 2 q^{13} + 7 q^{15} - 2 q^{17} + 2 q^{19} - 3 q^{21} - q^{23} - 37 q^{25} + 4 q^{27} - 6 q^{29} + 14 q^{31} + 5 q^{33} + 9 q^{35} - 2 q^{37} + 16 q^{39} - 2 q^{41} - 4 q^{43} + 13 q^{45} + 42 q^{47} - q^{49} - 19 q^{51} - 2 q^{53} + 18 q^{55} - 6 q^{57} - 70 q^{59} - 2 q^{61} + 2 q^{65} + 2 q^{67} - 31 q^{69} + 32 q^{71} - 2 q^{73} - 33 q^{75} + 21 q^{77} + 2 q^{79} - q^{81} + 28 q^{83} + 3 q^{85} + 31 q^{87} + 2 q^{89} - 4 q^{91} - 5 q^{93} - 54 q^{95} - 2 q^{97} + 61 q^{99} + O(q^{100}) \)

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.q.a 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
1008.2.q.b 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1008.2.q.c 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1008.2.q.d 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1008.2.q.e 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1008.2.q.f 1008.q 63.h $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1008.2.q.g 1008.q 63.h $6$ $8.049$ 6.0.309123.1 None \(0\) \(-2\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{4})q^{3}+(1-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1008.2.q.h 1008.q 63.h $6$ $8.049$ 6.0.309123.1 None \(0\) \(2\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+2\beta _{4}+\cdots)q^{5}+\cdots\)
1008.2.q.i 1008.q 63.h $10$ $8.049$ 10.0.\(\cdots\).1 None \(0\) \(1\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{8}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1008.2.q.j 1008.q 63.h $14$ $8.049$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-3\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{3}+\beta _{4}q^{5}+\beta _{12}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1008.2.q.k 1008.q 63.h $22$ $8.049$ None \(0\) \(-2\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$
1008.2.q.l 1008.q 63.h $22$ $8.049$ None \(0\) \(2\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \)