Properties

Label 475.2.v
Level $475$
Weight $2$
Character orbit 475.v
Rep. character $\chi_{475}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $384$
Newform subspaces $2$
Sturm bound $100$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(100\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

Total New Old
Modular forms 416 416 0
Cusp forms 384 384 0
Eisenstein series 32 32 0

Trace form

\( 384 q - 20 q^{4} - 18 q^{5} - 12 q^{6} - 14 q^{7} - 20 q^{9} + O(q^{10}) \) \( 384 q - 20 q^{4} - 18 q^{5} - 12 q^{6} - 14 q^{7} - 20 q^{9} - 12 q^{11} + 72 q^{16} - 36 q^{17} + 10 q^{19} - 52 q^{20} + 24 q^{23} + 2 q^{25} - 32 q^{26} - 28 q^{28} - 60 q^{30} + 4 q^{35} - 120 q^{36} + 16 q^{38} - 100 q^{39} - 20 q^{42} + 58 q^{43} - 160 q^{44} + 100 q^{45} - 82 q^{47} - 20 q^{54} + 20 q^{55} + 70 q^{57} - 72 q^{58} - 12 q^{61} + 72 q^{62} - 178 q^{63} + 40 q^{64} + 36 q^{66} + 148 q^{68} - 26 q^{73} - 32 q^{76} - 118 q^{77} + 296 q^{80} + 52 q^{81} - 108 q^{82} + 8 q^{83} - 100 q^{85} + 152 q^{87} - 216 q^{92} - 164 q^{93} + 84 q^{95} + 44 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.2.v.a 475.v 475.v $16$ $3.793$ 16.0.\(\cdots\).1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(-6\) $\mathrm{U}(1)[D_{20}]$ \(q+2\beta _{4}q^{4}+(1-\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
475.2.v.b 475.v 475.v $368$ $3.793$ None \(0\) \(0\) \(-16\) \(-8\) $\mathrm{SU}(2)[C_{20}]$