↑

Properties

Label 1152.3.z
Level $1152$
Weight $3$
Character orbit 1152.z
Rep. character $\chi_{1152}(31,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.z (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1600 400 1200
Cusp forms 1472 368 1104
Eisenstein series 128 32 96

Trace form

\( 368 q + 4 q^{5} + O(q^{10}) \) \( 368 q + 4 q^{5} + 4 q^{13} - 32 q^{17} - 28 q^{21} + 4 q^{29} - 16 q^{33} + 16 q^{37} + 108 q^{45} - 960 q^{49} + 16 q^{53} + 4 q^{61} - 8 q^{65} - 28 q^{69} - 388 q^{77} - 16 q^{81} + 104 q^{85} - 52 q^{93} - 8 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)