↑

Properties

Label 425.2.q
Level $425$
Weight $2$
Character orbit 425.q
Rep. character $\chi_{425}(84,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $176$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 425.q (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(425, [\chi])\).

Total New Old
Modular forms 192 192 0
Cusp forms 176 176 0
Eisenstein series 16 16 0

Trace form

\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} + O(q^{10}) \) \( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38} - 20 q^{42} + 40 q^{47} + 164 q^{49} + 84 q^{50} + 20 q^{51} - 30 q^{52} - 40 q^{53} - 18 q^{55} - 18 q^{59} - 48 q^{60} + 66 q^{64} + 80 q^{66} - 50 q^{67} + 68 q^{69} - 152 q^{70} + 60 q^{72} - 72 q^{76} - 40 q^{77} - 38 q^{81} + 50 q^{83} - 52 q^{84} + 47 q^{85} - 94 q^{86} - 120 q^{87} + 60 q^{89} + 50 q^{94} - 250 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
425.2.q.a 425.q 425.q $176$ $3.394$ None \(-10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$