Properties

Label 100.3.b
Level $100$
Weight $3$
Character orbit 100.b
Rep. character $\chi_{100}(51,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $6$
Sturm bound $45$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 100.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(45\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(100, [\chi])\).

Total New Old
Modular forms 36 22 14
Cusp forms 24 16 8
Eisenstein series 12 6 6

Trace form

\( 16q + 2q^{2} + 6q^{4} + 2q^{6} + 8q^{8} - 32q^{9} + O(q^{10}) \) \( 16q + 2q^{2} + 6q^{4} + 2q^{6} + 8q^{8} - 32q^{9} - 40q^{12} + 16q^{13} - 28q^{14} - 14q^{16} + 24q^{17} - 22q^{18} - 56q^{21} + 80q^{22} + 142q^{24} + 60q^{26} + 40q^{28} + 32q^{29} - 128q^{32} - 80q^{33} - 130q^{34} - 112q^{36} - 16q^{37} - 80q^{38} + 112q^{41} + 120q^{42} + 90q^{44} - 68q^{46} + 8q^{49} - 56q^{52} + 176q^{53} - 26q^{54} + 52q^{56} + 36q^{58} - 168q^{61} + 80q^{62} - 174q^{64} + 90q^{66} + 136q^{68} + 104q^{69} + 72q^{72} - 264q^{73} - 240q^{74} + 90q^{76} - 240q^{77} + 80q^{78} + 200q^{81} - 116q^{82} + 44q^{84} + 352q^{86} - 160q^{88} - 88q^{89} + 120q^{92} + 400q^{93} + 272q^{94} + 302q^{96} + 264q^{97} - 102q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
100.3.b.a \(1\) \(2.725\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+24q^{13}+\cdots\)
100.3.b.b \(1\) \(2.725\) \(\Q\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+4q^{4}+8q^{8}+9q^{9}-24q^{13}+\cdots\)
100.3.b.c \(2\) \(2.725\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-4q^{4}-8q^{6}+2iq^{7}+\cdots\)
100.3.b.d \(4\) \(2.725\) 4.0.8405.1 None \(-1\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
100.3.b.e \(4\) \(2.725\) 4.0.8405.1 None \(1\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
100.3.b.f \(4\) \(2.725\) \(\Q(\zeta_{10})\) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)