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Properties

Label 3024.2.z
Level $3024$
Weight $2$
Character orbit 3024.z
Rep. character $\chi_{3024}(757,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.z (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 1176 384 792
Cusp forms 1128 384 744
Eisenstein series 48 0 48

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 8 q^{10} - 40 q^{16} - 16 q^{19} + 16 q^{22} - 8 q^{34} - 32 q^{43} + 96 q^{46} - 384 q^{49} + 16 q^{52} + 32 q^{58} + 32 q^{61} - 64 q^{67} + 24 q^{70} - 96 q^{76} + 32 q^{79} - 40 q^{82} - 32 q^{85} + 200 q^{88} + 48 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)