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Properties

Label 1008.2.t
Level $1008$
Weight $2$
Character orbit 1008.t
Rep. character $\chi_{1008}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $92$
Newform subspaces $12$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (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: \(5\)
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

\( 92 q + q^{3} - 2 q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 92 q + q^{3} - 2 q^{5} + q^{7} - q^{9} + 2 q^{11} - 2 q^{13} + 7 q^{15} - 2 q^{17} + 2 q^{19} + 2 q^{23} + 74 q^{25} + 4 q^{27} - 6 q^{29} - 7 q^{31} - 13 q^{33} + 9 q^{35} - 2 q^{37} + 7 q^{39} - 2 q^{41} - 4 q^{43} - 17 q^{45} - 21 q^{47} - q^{49} - 13 q^{51} - 2 q^{53} + 18 q^{55} - 6 q^{57} + 35 q^{59} + q^{61} + 33 q^{63} - q^{65} - q^{67} - 31 q^{69} + 32 q^{71} - 2 q^{73} + 54 q^{75} - 21 q^{77} - q^{79} - 13 q^{81} + 28 q^{83} + 3 q^{85} - 14 q^{87} + 2 q^{89} - 4 q^{91} - 11 q^{93} + 27 q^{95} - 2 q^{97} + 61 q^{99} + O(q^{100}) \)

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.t.a 1008.t 63.g $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+\zeta_{6})q^{3}-q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1008.2.t.b 1008.t 63.g $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+2q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1008.2.t.c 1008.t 63.g $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}-3q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1008.2.t.d 1008.t 63.g $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}-q^{5}+(1-3\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
1008.2.t.e 1008.t 63.g $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+q^{5}+(3-\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
1008.2.t.f 1008.t 63.g $2$ $8.049$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(6\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+3q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1008.2.t.g 1008.t 63.g $6$ $8.049$ 6.0.309123.1 None \(0\) \(-4\) \(10\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{5})q^{3}+(2+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1008.2.t.h 1008.t 63.g $6$ $8.049$ 6.0.309123.1 None \(0\) \(-2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1008.2.t.i 1008.t 63.g $10$ $8.049$ 10.0.\(\cdots\).1 None \(0\) \(-2\) \(-8\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{7})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
1008.2.t.j 1008.t 63.g $14$ $8.049$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(4\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+\beta _{11}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots\)
1008.2.t.k 1008.t 63.g $22$ $8.049$ None \(0\) \(-2\) \(-6\) \(-7\) $\mathrm{SU}(2)[C_{3}]$
1008.2.t.l 1008.t 63.g $22$ $8.049$ None \(0\) \(2\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)