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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
475.2.v.a \(16\) \(3.793\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(-6\) \(q+2\beta _{4}q^{4}+(1-\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
475.2.v.b \(368\) \(3.793\) None \(0\) \(0\) \(-16\) \(-8\)