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Properties

Label 1100.2.bf
Level $1100$
Weight $2$
Character orbit 1100.bf
Rep. character $\chi_{1100}(39,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $704$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.bf (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1100 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1100, [\chi])\).

Total New Old
Modular forms 736 736 0
Cusp forms 704 704 0
Eisenstein series 32 32 0

Trace form

\( 704 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{8} - 170 q^{9} + O(q^{10}) \) \( 704 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{8} - 170 q^{9} + 20 q^{10} - 30 q^{12} - 10 q^{13} - 14 q^{14} - 5 q^{16} - 20 q^{17} - 15 q^{18} - 5 q^{20} - 25 q^{22} - 10 q^{24} - 14 q^{25} + 22 q^{26} - 5 q^{28} - 10 q^{29} - 25 q^{30} + 20 q^{33} - 8 q^{34} - 18 q^{36} + 5 q^{38} + 20 q^{40} - 10 q^{41} + 5 q^{42} - 32 q^{44} + 28 q^{45} - 5 q^{48} + 144 q^{49} + 40 q^{50} + 30 q^{52} + 30 q^{54} - 34 q^{56} - 55 q^{58} - 12 q^{60} - 10 q^{61} - 10 q^{62} - 25 q^{64} + 11 q^{66} - 75 q^{68} - 32 q^{69} + 69 q^{70} - 65 q^{72} - 10 q^{73} - 55 q^{74} - 10 q^{77} + 20 q^{78} - 34 q^{80} - 152 q^{81} - 10 q^{82} + 50 q^{85} + 31 q^{86} - 45 q^{88} - 12 q^{89} - 35 q^{90} - 5 q^{92} + 30 q^{93} - 85 q^{96} + 105 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

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