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Properties

Label 1152.3.u
Level $1152$
Weight $3$
Character orbit 1152.u
Rep. character $\chi_{1152}(271,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $156$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).

Total New Old
Modular forms 1600 164 1436
Cusp forms 1472 156 1316
Eisenstein series 128 8 120

Trace form

\( 156 q + 4 q^{5} + 4 q^{7} + O(q^{10}) \) \( 156 q + 4 q^{5} + 4 q^{7} - 4 q^{11} - 4 q^{13} + 4 q^{19} + 60 q^{23} - 4 q^{25} + 4 q^{29} - 100 q^{35} - 4 q^{37} + 4 q^{41} - 92 q^{43} - 8 q^{47} - 156 q^{53} + 260 q^{55} - 132 q^{59} + 60 q^{61} + 8 q^{65} + 36 q^{67} + 252 q^{71} - 4 q^{73} + 228 q^{77} - 504 q^{79} - 484 q^{83} + 96 q^{85} + 4 q^{89} - 188 q^{91} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)