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Properties

Label 1536.2.w
Level $1536$
Weight $2$
Character orbit 1536.w
Rep. character $\chi_{1536}(47,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $992$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1536 = 2^{9} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1536.w (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 384 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1536, [\chi])\).

Total New Old
Modular forms 4224 1056 3168
Cusp forms 3968 992 2976
Eisenstein series 256 64 192

Trace form

\( 992 q + 16 q^{3} + 32 q^{7} - 16 q^{9} + O(q^{10}) \) \( 992 q + 16 q^{3} + 32 q^{7} - 16 q^{9} - 32 q^{13} + 16 q^{15} + 32 q^{19} - 16 q^{21} - 32 q^{25} + 16 q^{27} + 32 q^{31} - 16 q^{33} - 32 q^{37} + 16 q^{39} + 32 q^{43} - 16 q^{45} - 32 q^{49} + 16 q^{51} + 32 q^{55} - 16 q^{57} - 32 q^{61} + 32 q^{63} + 32 q^{67} - 16 q^{69} - 32 q^{73} + 16 q^{75} + 32 q^{79} - 16 q^{81} - 32 q^{85} + 16 q^{87} + 32 q^{91} - 16 q^{93} - 32 q^{97} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1536, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces

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