Properties

Label 1008.2.v
Level 1008
Weight 2
Character orbit v
Rep. character \(\chi_{1008}(323,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 96
Newforms 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: \(\Q(i)\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.2.v.a \(4\) \(8.049\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}^{2}q^{2}-2q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots\)
1008.2.v.b \(4\) \(8.049\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{8}^{3}q^{2}+2q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots\)
1008.2.v.c \(12\) \(8.049\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-12\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
1008.2.v.d \(36\) \(8.049\) None \(0\) \(0\) \(0\) \(-36\)
1008.2.v.e \(40\) \(8.049\) None \(0\) \(0\) \(0\) \(40\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)