Properties

Label 1152.2.bg
Level $1152$
Weight $2$
Character orbit 1152.bg
Rep. character $\chi_{1152}(49,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $368$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.bg (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(384\)

Dimensions

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

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

Trace form

\( 368 q + 8 q^{3} - 4 q^{5} + 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 368 q + 8 q^{3} - 4 q^{5} + 4 q^{7} - 8 q^{9} + 4 q^{11} - 4 q^{13} + 16 q^{19} - 8 q^{21} + 4 q^{23} - 4 q^{25} + 32 q^{27} - 4 q^{29} + 8 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 32 q^{39} - 4 q^{41} + 4 q^{43} - 8 q^{45} - 16 q^{51} - 16 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} + 4 q^{67} - 8 q^{69} + 16 q^{71} - 16 q^{73} + 28 q^{75} - 4 q^{77} - 36 q^{83} + 16 q^{85} + 64 q^{87} - 16 q^{89} + 16 q^{91} + 4 q^{93} + 136 q^{95} - 8 q^{97} + 72 q^{99} + O(q^{100}) \)

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

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