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Properties

Label 3072.2.ba
Level $3072$
Weight $2$
Character orbit 3072.ba
Rep. character $\chi_{3072}(47,\cdot)$
Character field $\Q(\zeta_{64})$
Dimension $4032$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3072.ba (of order \(64\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 768 \)
Character field: \(\Q(\zeta_{64})\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 16640 4160 12480
Cusp forms 16128 4032 12096
Eisenstein series 512 128 384

Trace form

\( 4032 q + 32 q^{3} + 64 q^{7} - 32 q^{9} + O(q^{10}) \) \( 4032 q + 32 q^{3} + 64 q^{7} - 32 q^{9} - 64 q^{13} + 32 q^{15} + 64 q^{19} - 32 q^{21} - 64 q^{25} + 32 q^{27} + 64 q^{31} - 32 q^{33} - 64 q^{37} + 32 q^{39} + 64 q^{43} - 32 q^{45} - 64 q^{49} + 32 q^{51} + 64 q^{55} - 32 q^{57} - 64 q^{61} + 32 q^{63} + 64 q^{67} - 32 q^{69} - 64 q^{73} + 32 q^{75} + 64 q^{79} - 32 q^{81} - 64 q^{85} + 32 q^{87} + 64 q^{91} - 32 q^{93} - 64 q^{97} + 32 q^{99} + O(q^{100}) \)

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

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