Properties

Label 1008.2.b
Level $1008$
Weight $2$
Character orbit 1008.b
Rep. character $\chi_{1008}(559,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $9$
Sturm bound $384$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(384\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

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

Total New Old
Modular forms 216 20 196
Cusp forms 168 20 148
Eisenstein series 48 0 48

Trace form

\( 20 q + 4 q^{25} - 24 q^{29} + 8 q^{37} + 20 q^{49} + 24 q^{53} + 24 q^{77} + 48 q^{85}+O(q^{100}) \) Copy content Toggle raw display

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.b.a 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 336.2.b.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta-2)q^{7}-2\beta q^{11}-4\beta q^{17}-4 q^{19}+\cdots\)
1008.2.b.b 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 112.2.f.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta q^{5}+(-\beta-2)q^{7}+2\beta q^{11}+\cdots\)
1008.2.b.c 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 1008.2.b.c \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta-2)q^{7}-4\beta q^{13}+8 q^{19}+5 q^{25}+\cdots\)
1008.2.b.d 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-6}) \) None 336.2.b.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.e 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-6}) \) None 336.2.b.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+(1+\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.f 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 1008.2.b.c \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta+2)q^{7}-4\beta q^{13}-8 q^{19}+\cdots\)
1008.2.b.g 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 112.2.f.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta q^{5}+(\beta+2)q^{7}-2\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.h 1008.b 28.d $2$ $8.049$ \(\Q(\sqrt{-3}) \) None 336.2.b.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta+2)q^{7}-2\beta q^{11}+4\beta q^{17}+4 q^{19}+\cdots\)
1008.2.b.i 1008.b 28.d $4$ $8.049$ \(\Q(\sqrt{-6}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) 1008.2.b.i \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+3\beta _{1}q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)