Properties

Label 475.2.g
Level $475$
Weight $2$
Character orbit 475.g
Rep. character $\chi_{475}(18,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $4$
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.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
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 112 64 48
Cusp forms 88 56 32
Eisenstein series 24 8 16

Trace form

\( 56 q + 8 q^{6} + 6 q^{7} + O(q^{10}) \) \( 56 q + 8 q^{6} + 6 q^{7} + 8 q^{11} - 100 q^{16} - 6 q^{17} + 4 q^{23} - 56 q^{26} - 8 q^{28} + 92 q^{36} - 4 q^{38} - 2 q^{43} + 18 q^{47} + 88 q^{58} + 64 q^{61} - 8 q^{62} - 78 q^{63} - 272 q^{66} - 72 q^{68} - 6 q^{73} + 156 q^{76} + 62 q^{77} - 64 q^{81} - 88 q^{82} + 68 q^{83} - 88 q^{87} + 4 q^{92} + 96 q^{93} + 120 q^{96} + O(q^{100}) \)

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.g.a $4$ $3.793$ \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(-6\) \(q-2\beta _{1}q^{4}+(-2+2\beta _{1}+\beta _{3})q^{7}+3\beta _{1}q^{9}+\cdots\)
475.2.g.b $12$ $3.793$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots\)
475.2.g.c $16$ $3.793$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2\beta _{7}-\beta _{10})q^{4}+\cdots\)
475.2.g.d $24$ $3.793$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)