Properties

Label 1008.2.bt
Level $1008$
Weight $2$
Character orbit 1008.bt
Rep. character $\chi_{1008}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $4$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 432 32 400
Cusp forms 336 32 304
Eisenstein series 96 0 96

Trace form

\( 32 q + 4 q^{7} + O(q^{10}) \) \( 32 q + 4 q^{7} - 12 q^{19} - 8 q^{25} - 12 q^{31} + 8 q^{43} - 4 q^{67} + 24 q^{73} + 36 q^{79} - 32 q^{85} + 36 q^{91} + O(q^{100}) \)

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.bt.a 1008.bt 21.g $4$ $8.049$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 252.2.t.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{5}+(-2+3\beta _{1})q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots\)
1008.2.bt.b 1008.bt 21.g $4$ $8.049$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 63.2.p.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{3})q^{5}+(2-3\beta _{2})q^{7}+\beta _{1}q^{11}+\cdots\)
1008.2.bt.c 1008.bt 21.g $8$ $8.049$ \(\Q(\zeta_{24})\) None 126.2.k.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}+(-\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
1008.2.bt.d 1008.bt 21.g $16$ $8.049$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 504.2.bl.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{10})q^{5}+(\beta _{3}+\beta _{9})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)

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

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