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Properties

Label 3072.2.w
Level $3072$
Weight $2$
Character orbit 3072.w
Rep. character $\chi_{3072}(95,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $1984$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3072.w (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 384 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).

Total New Old
Modular forms 8448 2112 6336
Cusp forms 7936 1984 5952
Eisenstein series 512 128 384

Trace form

\( 1984 q - 32 q^{9} + O(q^{10}) \) \( 1984 q - 32 q^{9} + 64 q^{13} + 32 q^{21} - 64 q^{25} - 32 q^{33} + 64 q^{37} + 32 q^{45} - 64 q^{49} - 32 q^{57} + 64 q^{61} + 32 q^{69} - 64 q^{73} - 32 q^{81} + 64 q^{85} + 32 q^{93} - 64 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)