Properties

Label 93.2.p
Level $93$
Weight $2$
Character orbit 93.p
Rep. character $\chi_{93}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $72$
Newform subspaces $2$
Sturm bound $21$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.p (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(93, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 72 72 0
Eisenstein series 32 32 0

Trace form

\( 72q - 7q^{3} + 8q^{4} - 9q^{6} - 30q^{7} - 11q^{9} + O(q^{10}) \) \( 72q - 7q^{3} + 8q^{4} - 9q^{6} - 30q^{7} - 11q^{9} - 36q^{10} + 21q^{12} - 23q^{13} - 20q^{15} - 32q^{16} - 6q^{18} + 7q^{19} - 28q^{21} - 24q^{22} - 48q^{24} + 18q^{25} + 5q^{27} + 58q^{28} + 26q^{31} - 7q^{33} - 4q^{34} + 19q^{36} + 57q^{37} + 20q^{39} + 8q^{40} + 15q^{42} - 48q^{43} - 63q^{45} - 70q^{46} + 24q^{48} + 7q^{49} + 58q^{51} + 90q^{52} + 100q^{54} + 10q^{55} + 72q^{57} + 50q^{58} + 85q^{60} - 42q^{63} + 30q^{64} + 6q^{66} - 30q^{67} + 110q^{69} - 158q^{70} + 163q^{72} - 27q^{73} + 40q^{75} - 32q^{76} - 11q^{78} - 11q^{79} - 99q^{81} - 116q^{82} - 56q^{84} - 130q^{85} - 9q^{87} - 222q^{88} - 93q^{90} - 25q^{91} - 106q^{93} + 128q^{94} - 122q^{96} + 33q^{97} - 102q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(93, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
93.2.p.a \(8\) \(0.743\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-4\) \(q+(\zeta_{15}^{2}+2\zeta_{15}^{7})q^{3}+2\zeta_{15}^{6}q^{4}+\cdots\)
93.2.p.b \(64\) \(0.743\) None \(0\) \(-10\) \(0\) \(-26\)