Properties

Label 1008.1.u
Level $1008$
Weight $1$
Character orbit 1008.u
Rep. character $\chi_{1008}(181,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $3$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1008.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1008, [\chi])\).

Total New Old
Modular forms 28 10 18
Cusp forms 12 6 6
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + 2 q^{4} + 2 q^{11} + 2 q^{14} + 6 q^{16} - 2 q^{22} + 2 q^{29} + 2 q^{37} - 2 q^{43} - 2 q^{44} - 6 q^{49} + 2 q^{50} - 2 q^{53} - 2 q^{56} - 6 q^{58} + 2 q^{64} + 6 q^{67} - 2 q^{74} - 2 q^{77} + 2 q^{86}+ \cdots - 6 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.1.u.a 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None 1008.1.u.a \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+i q^{7}-q^{8}+(-i+1)q^{11}+\cdots\)
1008.1.u.b 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None 112.1.l.a \(0\) \(0\) \(0\) \(0\) \(q+i q^{2}-q^{4}-i q^{7}-i q^{8}+(-i+1)q^{11}+\cdots\)
1008.1.u.c 1008.u 112.l $2$ $0.503$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None 1008.1.u.a \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+i q^{7}+q^{8}+(i-1)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)