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Properties

Label 1152.2.y
Level $1152$
Weight $2$
Character orbit 1152.y
Rep. character $\chi_{1152}(95,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

Total New Old
Modular forms 832 208 624
Cusp forms 704 176 528
Eisenstein series 128 32 96

Trace form

\( 176 q + 12 q^{5} + O(q^{10}) \) \( 176 q + 12 q^{5} + 4 q^{13} - 4 q^{21} + 12 q^{29} - 16 q^{33} + 16 q^{37} - 12 q^{45} - 48 q^{49} + 4 q^{61} - 24 q^{65} + 20 q^{69} + 12 q^{77} - 16 q^{81} - 16 q^{85} + 68 q^{93} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

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