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Properties

Label 1100.2.cq
Level $1100$
Weight $2$
Character orbit 1100.cq
Rep. character $\chi_{1100}(23,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1200$
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.cq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 1472 1200 272
Cusp forms 1408 1200 208
Eisenstein series 64 0 64

Trace form

\( 1200 q + 12 q^{8} + O(q^{10}) \) \( 1200 q + 12 q^{8} + 4 q^{13} + 20 q^{17} - 28 q^{18} + 20 q^{25} + 20 q^{28} + 40 q^{30} + 40 q^{32} - 20 q^{37} - 20 q^{38} - 40 q^{40} - 200 q^{42} - 20 q^{45} - 268 q^{48} - 184 q^{50} - 184 q^{52} + 20 q^{53} - 260 q^{54} + 32 q^{57} + 8 q^{58} - 120 q^{60} + 36 q^{62} - 60 q^{64} + 12 q^{65} - 52 q^{68} - 16 q^{70} + 20 q^{72} - 52 q^{73} + 16 q^{80} + 300 q^{81} + 80 q^{82} + 160 q^{84} - 80 q^{85} + 96 q^{88} - 260 q^{89} + 240 q^{90} + 44 q^{92} - 24 q^{93} - 40 q^{96} - 20 q^{97} + 64 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)