Properties

Label 100.2.l
Level $100$
Weight $2$
Character orbit 100.l
Rep. character $\chi_{100}(3,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $104$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 100.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).

Total New Old
Modular forms 136 136 0
Cusp forms 104 104 0
Eisenstein series 32 32 0

Trace form

\( 104q - 8q^{2} - 10q^{4} - 16q^{5} - 6q^{6} - 14q^{8} - 20q^{9} + O(q^{10}) \) \( 104q - 8q^{2} - 10q^{4} - 16q^{5} - 6q^{6} - 14q^{8} - 20q^{9} - 16q^{10} - 10q^{12} - 18q^{13} - 10q^{14} - 6q^{16} - 26q^{17} - 4q^{18} - 6q^{20} - 12q^{21} - 10q^{22} - 26q^{25} - 16q^{26} - 10q^{28} - 20q^{29} - 10q^{30} - 18q^{32} - 20q^{33} - 10q^{34} - 22q^{36} - 6q^{37} + 20q^{38} + 44q^{40} - 12q^{41} + 90q^{42} + 60q^{44} - 26q^{45} - 6q^{46} + 120q^{48} + 94q^{50} + 84q^{52} - 38q^{53} + 120q^{54} - 6q^{56} - 20q^{57} + 52q^{58} + 90q^{60} - 12q^{61} + 40q^{62} + 20q^{64} - 22q^{65} - 30q^{66} + 2q^{68} - 20q^{69} - 10q^{70} - 28q^{72} + 2q^{73} - 20q^{77} + 20q^{78} - 26q^{80} - 18q^{81} - 66q^{82} - 90q^{84} + 48q^{85} - 6q^{86} - 130q^{88} + 110q^{89} - 166q^{90} - 110q^{92} + 60q^{93} - 170q^{94} + 14q^{96} + 154q^{97} - 144q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
100.2.l.a \(8\) \(0.799\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(4\) \(0\) \(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
100.2.l.b \(96\) \(0.799\) None \(-10\) \(0\) \(-20\) \(0\)