Properties

Label 531.5.c
Level $531$
Weight $5$
Character orbit 531.c
Rep. character $\chi_{531}(235,\cdot)$
Character field $\Q$
Dimension $99$
Newform subspaces $4$
Sturm bound $300$
Trace bound $16$

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Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 531.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(300\)
Trace bound: \(16\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(531, [\chi])\).

Total New Old
Modular forms 244 101 143
Cusp forms 236 99 137
Eisenstein series 8 2 6

Trace form

\( 99q - 786q^{4} - 4q^{5} + 78q^{7} + O(q^{10}) \) \( 99q - 786q^{4} - 4q^{5} + 78q^{7} + 5902q^{16} + 563q^{17} - 632q^{19} + 452q^{20} + 1430q^{22} + 9983q^{25} - 870q^{26} - 1462q^{28} + 500q^{29} - 6035q^{35} + 434q^{41} + 4044q^{46} + 31417q^{49} + 11744q^{53} + 9823q^{59} - 16740q^{62} - 52534q^{64} - 22366q^{68} + 3239q^{71} - 510q^{74} + 11224q^{76} + 10834q^{79} - 26848q^{80} + 9644q^{85} + 58866q^{86} - 13726q^{88} - 35048q^{94} - 12722q^{95} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(531, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
531.5.c.a \(3\) \(54.889\) 3.3.1593.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{4}q^{4}+(2\beta _{1}+9\beta _{2})q^{5}+(7\beta _{1}+15\beta _{2})q^{7}+\cdots\)
531.5.c.b \(16\) \(54.889\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-4\) \(-82\) \(q+\beta _{1}q^{2}+(-12+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
531.5.c.c \(40\) \(54.889\) None \(0\) \(0\) \(0\) \(80\)
531.5.c.d \(40\) \(54.889\) None \(0\) \(0\) \(0\) \(80\)

Decomposition of \(S_{5}^{\mathrm{old}}(531, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(531, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)