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Properties

Label 59.5.b
Level $59$
Weight $5$
Character orbit 59.b
Rep. character $\chi_{59}(58,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $2$
Sturm bound $25$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 59.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(59, [\chi])\).

Total New Old
Modular forms 21 21 0
Cusp forms 19 19 0
Eisenstein series 2 2 0

Trace form

\( 19q - 20q^{3} - 146q^{4} + 4q^{5} - 82q^{7} + 359q^{9} + O(q^{10}) \) \( 19q - 20q^{3} - 146q^{4} + 4q^{5} - 82q^{7} + 359q^{9} + 220q^{12} + 735q^{15} + 222q^{16} - 35q^{17} - 632q^{19} - 896q^{20} - 665q^{21} - 410q^{22} + 2191q^{25} + 2322q^{26} - 4241q^{27} + 618q^{28} + 496q^{29} - 4285q^{35} + 462q^{36} + 4762q^{41} - 2717q^{45} + 5676q^{46} - 8588q^{48} + 10361q^{49} - 8168q^{51} - 9560q^{53} + 63q^{57} + 1913q^{59} + 13696q^{60} + 1500q^{62} - 2000q^{63} + 22106q^{64} + 8864q^{66} - 7202q^{68} + 2725q^{71} - 13866q^{74} + 5890q^{75} - 8888q^{76} - 50872q^{78} - 25574q^{79} - 6248q^{80} + 51987q^{81} - 24056q^{84} - 18364q^{85} + 7014q^{86} + 42247q^{87} - 2294q^{88} - 7528q^{94} + 1718q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(59, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
59.5.b.a \(3\) \(6.099\) 3.3.1593.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) \(q+(4\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(5\beta _{1}-11\beta _{2})q^{5}+\cdots\)
59.5.b.b \(16\) \(6.099\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-20\) \(4\) \(-82\) \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-12+\beta _{2}+\cdots)q^{4}+\cdots\)