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Properties

Label 625.2.e
Level $625$
Weight $2$
Character orbit 625.e
Rep. character $\chi_{625}(124,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $136$
Newform subspaces $11$
Sturm bound $125$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.e (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 11 \)
Sturm bound: \(125\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(625, [\chi])\).

Total New Old
Modular forms 312 184 128
Cusp forms 192 136 56
Eisenstein series 120 48 72

Trace form

\( 136 q + 28 q^{4} + 12 q^{6} + 22 q^{9} + O(q^{10}) \) \( 136 q + 28 q^{4} + 12 q^{6} + 22 q^{9} + 12 q^{11} - 24 q^{14} - 4 q^{16} + 12 q^{21} + 40 q^{24} - 68 q^{26} + 20 q^{29} + 12 q^{31} - 14 q^{34} - 24 q^{36} + 24 q^{39} - 8 q^{41} + 16 q^{44} + 12 q^{46} + 8 q^{49} - 48 q^{51} - 60 q^{54} - 20 q^{56} - 8 q^{61} - 32 q^{64} - 36 q^{66} - 36 q^{69} - 28 q^{71} + 36 q^{74} - 80 q^{76} - 14 q^{81} - 104 q^{84} + 12 q^{86} + 10 q^{89} + 12 q^{91} + 106 q^{94} - 78 q^{96} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(625, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
625.2.e.a 625.e 25.e $8$ $4.991$ 8.0.58140625.2 None \(0\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}+\beta _{5}+\beta _{7})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
625.2.e.b 625.e 25.e $8$ $4.991$ 8.0.484000000.6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1+\beta _{2}-3\beta _{3}+\cdots)q^{4}+\cdots\)
625.2.e.c 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+(-1+\cdots)q^{4}+\cdots\)
625.2.e.d 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(\zeta_{20}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}+\cdots\)
625.2.e.e 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)
625.2.e.f 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(\zeta_{20}+\cdots)q^{3}+\cdots\)
625.2.e.g 625.e 25.e $8$ $4.991$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\cdots)q^{3}+\cdots\)
625.2.e.h 625.e 25.e $8$ $4.991$ 8.0.484000000.6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{1}-\beta _{6})q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
625.2.e.i 625.e 25.e $8$ $4.991$ 8.0.58140625.2 None \(0\) \(5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\beta _{4}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{3}+\cdots\)
625.2.e.j 625.e 25.e $32$ $4.991$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
625.2.e.k 625.e 25.e $32$ $4.991$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(625, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(625, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)