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Properties

Label 1100.2.df
Level $1100$
Weight $2$
Character orbit 1100.df
Rep. character $\chi_{1100}(73,\cdot)$
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.df (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

\( 240 q - 8 q^{3} + 4 q^{5} - 10 q^{9} + O(q^{10}) \) \( 240 q - 8 q^{3} + 4 q^{5} - 10 q^{9} - 20 q^{13} + 4 q^{15} + 10 q^{17} + 6 q^{23} + 14 q^{25} + 10 q^{27} - 22 q^{33} - 30 q^{35} + 6 q^{37} - 26 q^{45} - 12 q^{47} + 30 q^{49} + 16 q^{53} + 32 q^{55} - 40 q^{57} + 80 q^{63} - 42 q^{67} + 20 q^{71} + 140 q^{75} + 44 q^{77} - 80 q^{79} + 30 q^{81} - 20 q^{85} + 6 q^{93} + 6 q^{97} - 130 q^{99} + O(q^{100}) \)

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

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