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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
531.5.c.a 531.c 59.b $3$ $54.889$ 3.3.1593.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{4}+(2\beta _{1}+9\beta _{2})q^{5}+(7\beta _{1}+15\beta _{2})q^{7}+\cdots\)
531.5.c.b 531.c 59.b $16$ $54.889$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-4\) \(-82\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-12+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
531.5.c.c 531.c 59.b $40$ $54.889$ None \(0\) \(0\) \(0\) \(80\) $\mathrm{SU}(2)[C_{2}]$
531.5.c.d 531.c 59.b $40$ $54.889$ None \(0\) \(0\) \(0\) \(80\) $\mathrm{SU}(2)[C_{2}]$

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

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