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Properties

Label 1008.2.v
Level $1008$
Weight $2$
Character orbit 1008.v
Rep. character $\chi_{1008}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $5$
Sturm bound $384$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(4\)
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 400 96 304
Cusp forms 368 96 272
Eisenstein series 32 0 32

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 16 q^{10} + 24 q^{16} - 32 q^{19} + 32 q^{22} + 16 q^{34} + 64 q^{43} - 80 q^{46} + 96 q^{49} - 96 q^{52} + 128 q^{55} + 8 q^{58} + 64 q^{61} + 16 q^{67} + 48 q^{70} - 48 q^{76} - 80 q^{82} + 64 q^{85} - 104 q^{88} - 96 q^{94} + O(q^{100}) \)

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.v.a 1008.v 48.k $4$ $8.049$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}-2q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots\)
1008.2.v.b 1008.v 48.k $4$ $8.049$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}+2q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots\)
1008.2.v.c 1008.v 48.k $12$ $8.049$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
1008.2.v.d 1008.v 48.k $36$ $8.049$ None \(0\) \(0\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{4}]$
1008.2.v.e 1008.v 48.k $40$ $8.049$ None \(0\) \(0\) \(0\) \(40\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)