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Properties

Label 1805.2.x
Level $1805$
Weight $2$
Character orbit 1805.x
Rep. character $\chi_{1805}(18,\cdot)$
Character field $\Q(\zeta_{76})$
Dimension $6768$
Sturm bound $380$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.x (of order \(76\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1805 \)
Character field: \(\Q(\zeta_{76})\)
Sturm bound: \(380\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1805, [\chi])\).

Total New Old
Modular forms 6912 6912 0
Cusp forms 6768 6768 0
Eisenstein series 144 144 0

Trace form

\( 6768 q - 38 q^{2} - 38 q^{3} - 34 q^{5} - 60 q^{6} - 34 q^{7} - 38 q^{8} + O(q^{10}) \) \( 6768 q - 38 q^{2} - 38 q^{3} - 34 q^{5} - 60 q^{6} - 34 q^{7} - 38 q^{8} - 38 q^{10} - 60 q^{11} - 38 q^{12} - 38 q^{13} - 38 q^{15} + 272 q^{16} - 46 q^{17} - 38 q^{18} - 70 q^{20} - 76 q^{21} - 228 q^{22} - 26 q^{23} - 18 q^{25} - 76 q^{26} - 38 q^{27} - 92 q^{28} + 2 q^{30} - 76 q^{31} - 38 q^{32} - 114 q^{33} - 22 q^{35} - 424 q^{36} - 38 q^{37} - 42 q^{38} - 38 q^{40} - 76 q^{41} - 38 q^{42} - 126 q^{43} - 268 q^{45} - 22 q^{47} - 38 q^{48} + 114 q^{50} - 228 q^{51} - 38 q^{52} - 38 q^{53} - 78 q^{55} + 152 q^{56} - 38 q^{57} + 50 q^{58} - 38 q^{60} - 52 q^{61} - 84 q^{62} - 106 q^{63} + 114 q^{65} - 52 q^{66} - 38 q^{67} - 156 q^{68} - 38 q^{70} - 76 q^{71} - 38 q^{72} - 54 q^{73} - 38 q^{75} - 56 q^{76} + 42 q^{77} - 38 q^{78} - 22 q^{80} + 260 q^{81} - 126 q^{82} + 22 q^{83} - 18 q^{85} + 608 q^{86} - 126 q^{87} - 38 q^{88} - 38 q^{90} - 152 q^{91} - 54 q^{92} + 58 q^{93} - 176 q^{95} + 720 q^{96} - 38 q^{97} - 38 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces

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