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Properties

Label 1100.2.ch
Level $1100$
Weight $2$
Character orbit 1100.ch
Rep. character $\chi_{1100}(79,\cdot)$
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.ch (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

\( 704 q - 5 q^{2} - q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{8} + 660 q^{9} + O(q^{10}) \) \( 704 q - 5 q^{2} - q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{8} + 660 q^{9} + 10 q^{10} + 10 q^{12} - 20 q^{13} - 9 q^{14} - 5 q^{16} - 10 q^{17} - 15 q^{18} - 5 q^{20} - 30 q^{21} - 10 q^{22} - 10 q^{24} - 14 q^{25} - 23 q^{26} - 5 q^{28} - 10 q^{29} - 20 q^{30} - 50 q^{32} - 20 q^{33} - 8 q^{34} - 8 q^{36} - 10 q^{37} - 5 q^{38} - 5 q^{40} - 10 q^{41} - 65 q^{42} + 3 q^{44} - 52 q^{45} - 5 q^{46} - 20 q^{48} + 144 q^{49} + 30 q^{50} - 5 q^{52} - 10 q^{53} - 65 q^{54} + q^{56} + 30 q^{58} - 27 q^{60} + 70 q^{62} + 35 q^{64} - 50 q^{65} + q^{66} - 35 q^{68} + 28 q^{69} + 9 q^{70} - 60 q^{72} - 10 q^{73} + 35 q^{74} - 10 q^{77} - 55 q^{78} - 69 q^{80} + 528 q^{81} + 60 q^{82} - 70 q^{84} - 50 q^{85} - 19 q^{86} - 60 q^{88} - 12 q^{89} + 75 q^{90} - 30 q^{93} - 50 q^{94} - 10 q^{97} + 10 q^{98} + O(q^{100}) \)

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.