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Properties

Label 1100.2.cc
Level $1100$
Weight $2$
Character orbit 1100.cc
Rep. character $\chi_{1100}(389,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $120$
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.cc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
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 744 120 624
Cusp forms 696 120 576
Eisenstein series 48 0 48

Trace form

\( 120 q - 5 q^{3} + q^{5} - 5 q^{7} + 27 q^{9} + O(q^{10}) \) \( 120 q - 5 q^{3} + q^{5} - 5 q^{7} + 27 q^{9} - 2 q^{11} - 11 q^{15} - 5 q^{17} + 24 q^{19} + 8 q^{21} - 3 q^{25} + 10 q^{27} + 48 q^{29} - 8 q^{31} + 25 q^{33} - 13 q^{35} + 35 q^{37} + 20 q^{39} + 4 q^{41} + 30 q^{45} - 35 q^{47} + 27 q^{49} + 8 q^{51} + 10 q^{53} - 8 q^{55} + 20 q^{57} + 14 q^{59} + 17 q^{61} + 115 q^{63} - 7 q^{65} + 55 q^{67} - 6 q^{69} + 30 q^{71} + 15 q^{73} + 33 q^{75} + 5 q^{77} + 8 q^{79} - 43 q^{81} - 30 q^{83} + 13 q^{85} + 10 q^{89} + 19 q^{91} - 40 q^{93} - 28 q^{95} + 5 q^{97} - 59 q^{99} + O(q^{100}) \)

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

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