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Properties

Label 1120.2.dz
Level $1120$
Weight $2$
Character orbit 1120.dz
Rep. character $\chi_{1120}(157,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1504$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.dz (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1120 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1120, [\chi])\).

Total New Old
Modular forms 1568 1568 0
Cusp forms 1504 1504 0
Eisenstein series 64 64 0

Trace form

\( 1504 q - 4 q^{2} - 12 q^{3} - 12 q^{5} - 16 q^{7} - 40 q^{8} + O(q^{10}) \) \( 1504 q - 4 q^{2} - 12 q^{3} - 12 q^{5} - 16 q^{7} - 40 q^{8} + 24 q^{10} - 8 q^{11} - 12 q^{12} + 16 q^{14} - 8 q^{16} - 20 q^{18} - 16 q^{21} - 16 q^{22} - 8 q^{23} - 4 q^{25} - 24 q^{26} + 8 q^{28} + 36 q^{30} - 48 q^{31} - 4 q^{32} - 24 q^{33} - 4 q^{35} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 12 q^{40} + 80 q^{42} - 16 q^{43} + 16 q^{44} - 12 q^{45} - 8 q^{46} - 8 q^{51} - 120 q^{52} - 4 q^{53} - 168 q^{54} - 16 q^{56} - 32 q^{57} + 28 q^{58} - 20 q^{60} - 24 q^{61} - 16 q^{63} + 96 q^{64} - 8 q^{65} - 168 q^{66} - 28 q^{67} - 12 q^{68} + 32 q^{71} - 36 q^{72} - 24 q^{73} - 12 q^{75} + 20 q^{77} - 56 q^{78} - 12 q^{80} - 156 q^{82} - 56 q^{84} - 16 q^{85} - 8 q^{86} - 48 q^{88} - 16 q^{91} - 56 q^{92} - 28 q^{93} - 8 q^{95} - 24 q^{96} + 56 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1120, [\chi])\) into newform subspaces

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