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Properties

Label 125.5.c
Level $125$
Weight $5$
Character orbit 125.c
Rep. character $\chi_{125}(57,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $2$
Sturm bound $62$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 125.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(62\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(125, [\chi])\).

Total New Old
Modular forms 110 64 46
Cusp forms 90 64 26
Eisenstein series 20 0 20

Trace form

\( 64 q + 28 q^{6} + O(q^{10}) \) \( 64 q + 28 q^{6} - 12 q^{11} - 4676 q^{16} + 4588 q^{21} - 1512 q^{26} - 2492 q^{31} + 14784 q^{36} - 1932 q^{41} + 30548 q^{46} - 23492 q^{51} - 50820 q^{56} - 18612 q^{61} + 70276 q^{66} - 4152 q^{71} - 43340 q^{76} - 61176 q^{81} - 41532 q^{86} + 209348 q^{91} + 65568 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(125, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
125.5.c.a 125.c 5.c $32$ $12.921$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
125.5.c.b 125.c 5.c $32$ $12.921$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(125, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(125, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)