Properties

Label 475.3.c
Level $475$
Weight $3$
Character orbit 475.c
Rep. character $\chi_{475}(151,\cdot)$
Character field $\Q$
Dimension $61$
Newform subspaces $9$
Sturm bound $150$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(150\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(475, [\chi])\).

Total New Old
Modular forms 106 67 39
Cusp forms 94 61 33
Eisenstein series 12 6 6

Trace form

\( 61q - 114q^{4} - 18q^{6} - 5q^{7} - 157q^{9} + O(q^{10}) \) \( 61q - 114q^{4} - 18q^{6} - 5q^{7} - 157q^{9} - 15q^{11} + 174q^{16} - q^{17} + 45q^{19} - 76q^{23} + 138q^{24} - 34q^{26} - 34q^{28} + 68q^{36} + 174q^{38} - 146q^{39} + 30q^{42} - 195q^{43} - 24q^{44} - 39q^{47} + 304q^{49} + 250q^{54} - 190q^{57} + 62q^{58} + 141q^{61} + 116q^{62} + 101q^{63} - 578q^{64} + 244q^{66} + 550q^{68} + 59q^{73} - 276q^{74} - 446q^{76} + 115q^{77} + 905q^{81} - 164q^{82} + 150q^{83} - 574q^{87} + 34q^{92} - 36q^{93} - 742q^{96} + 613q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
475.3.c.a \(1\) \(12.943\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(5\) \(q+4q^{4}+5q^{7}+9q^{9}+3q^{11}+2^{4}q^{16}+\cdots\)
475.3.c.b \(2\) \(12.943\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(10\) \(q+\beta q^{2}-\beta q^{3}-9q^{4}+13q^{6}+5q^{7}+\cdots\)
475.3.c.c \(2\) \(12.943\) \(\Q(\sqrt{19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+4q^{4}-3\beta q^{7}+9q^{9}-3q^{11}+2^{4}q^{16}+\cdots\)
475.3.c.d \(4\) \(12.943\) 4.0.7600.1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(-4+3\beta _{3})q^{4}+\cdots\)
475.3.c.e \(4\) \(12.943\) 4.0.462080.1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+\beta _{3})q^{4}+\cdots\)
475.3.c.f \(8\) \(12.943\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+2\beta _{4})q^{4}+\cdots\)
475.3.c.g \(12\) \(12.943\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
475.3.c.h \(14\) \(12.943\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{6}+\cdots\)
475.3.c.i \(14\) \(12.943\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(20\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)