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Properties

Label 1008.3.w
Level $1008$
Weight $3$
Character orbit 1008.w
Rep. character $\chi_{1008}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 784 192 592
Cusp forms 752 192 560
Eisenstein series 32 0 32

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 80 q^{10} - 104 q^{16} - 128 q^{19} + 224 q^{22} + 176 q^{34} - 256 q^{43} - 48 q^{46} - 1344 q^{49} - 736 q^{52} - 104 q^{58} - 128 q^{61} + 64 q^{67} + 336 q^{70} + 912 q^{76} + 1024 q^{79} + 400 q^{82} - 640 q^{85} + 664 q^{88} + 96 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)