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Properties

Label 1100.2.ct
Level $1100$
Weight $2$
Character orbit 1100.ct
Rep. character $\chi_{1100}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
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.ct (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
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 1488 240 1248
Cusp forms 1392 240 1152
Eisenstein series 96 0 96

Trace form

\( 240 q + 2 q^{3} - 6 q^{5} + 20 q^{7} + 10 q^{9} + O(q^{10}) \) \( 240 q + 2 q^{3} - 6 q^{5} + 20 q^{7} + 10 q^{9} - 16 q^{15} + 10 q^{17} - 14 q^{23} + 4 q^{25} - 10 q^{27} + 38 q^{33} + 30 q^{35} + 66 q^{37} + 50 q^{39} - 50 q^{43} - 26 q^{45} + 28 q^{47} + 20 q^{49} + 36 q^{53} - 18 q^{55} - 80 q^{57} + 100 q^{65} + 38 q^{67} - 20 q^{69} - 30 q^{71} + 60 q^{75} + 44 q^{77} + 160 q^{79} + 30 q^{81} - 100 q^{83} - 20 q^{85} - 100 q^{87} - 50 q^{89} + 46 q^{93} - 40 q^{95} - 54 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)