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Properties

Label 1152.2.bl
Level $1152$
Weight $2$
Character orbit 1152.bl
Rep. character $\chi_{1152}(37,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $1264$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.bl (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 3136 1296 1840
Cusp forms 3008 1264 1744
Eisenstein series 128 32 96

Trace form

\( 1264 q + 16 q^{2} - 16 q^{4} + 16 q^{5} - 16 q^{7} + 16 q^{8} + O(q^{10}) \) \( 1264 q + 16 q^{2} - 16 q^{4} + 16 q^{5} - 16 q^{7} + 16 q^{8} - 16 q^{10} + 16 q^{11} - 16 q^{13} + 16 q^{14} - 16 q^{16} + 16 q^{17} - 16 q^{19} + 16 q^{20} - 16 q^{22} + 16 q^{23} - 16 q^{25} + 16 q^{26} - 16 q^{28} + 16 q^{29} - 16 q^{31} + 16 q^{32} - 16 q^{34} + 16 q^{35} - 16 q^{37} + 16 q^{38} - 16 q^{40} + 16 q^{41} - 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{47} - 16 q^{49} + 64 q^{50} - 112 q^{52} + 16 q^{53} - 16 q^{55} + 128 q^{56} + 128 q^{58} + 16 q^{59} - 16 q^{61} + 112 q^{62} - 208 q^{64} - 16 q^{67} + 112 q^{68} - 208 q^{70} + 16 q^{71} - 16 q^{73} + 128 q^{74} + 48 q^{76} + 16 q^{77} - 16 q^{79} + 64 q^{80} - 16 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{88} + 16 q^{89} - 16 q^{91} + 16 q^{92} - 16 q^{94} + 16 q^{95} - 16 q^{97} + 16 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)