Properties

Label 475.2.l
Level $475$
Weight $2$
Character orbit 475.l
Rep. character $\chi_{475}(101,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $174$
Newform subspaces $6$
Sturm bound $100$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 6 \)
Sturm bound: \(100\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 336 210 126
Cusp forms 264 174 90
Eisenstein series 72 36 36

Trace form

\( 174 q + 6 q^{2} + 9 q^{3} - 21 q^{6} + 12 q^{8} + 15 q^{9} + O(q^{10}) \) \( 174 q + 6 q^{2} + 9 q^{3} - 21 q^{6} + 12 q^{8} + 15 q^{9} - 12 q^{11} + 9 q^{12} + 9 q^{13} + 27 q^{14} - 6 q^{16} - 3 q^{17} - 30 q^{18} - 12 q^{19} - 42 q^{21} - 24 q^{22} - 18 q^{23} + 63 q^{24} - 27 q^{26} + 12 q^{27} + 30 q^{28} - 3 q^{29} - 33 q^{31} - 69 q^{32} + 45 q^{33} - 36 q^{34} - 78 q^{36} + 24 q^{37} + 63 q^{38} - 48 q^{39} - 27 q^{41} - 27 q^{42} + 45 q^{43} - 39 q^{44} - 24 q^{46} - 51 q^{47} + 33 q^{48} - 57 q^{49} + 21 q^{51} + 15 q^{52} - 9 q^{53} - 66 q^{54} + 30 q^{56} - 66 q^{57} - 84 q^{58} - 6 q^{59} + 30 q^{61} + 24 q^{62} - 90 q^{63} + 81 q^{66} + 54 q^{67} - 33 q^{68} - 6 q^{69} - 30 q^{71} + 60 q^{72} - 18 q^{73} + 21 q^{74} - 132 q^{76} + 54 q^{77} - 39 q^{78} - 75 q^{79} - 72 q^{81} + 126 q^{82} + 165 q^{84} - 108 q^{86} + 81 q^{87} - 21 q^{88} + 108 q^{89} - 57 q^{91} + 66 q^{92} - 9 q^{93} - 18 q^{94} + 138 q^{96} + 42 q^{97} - 27 q^{98} - 81 q^{99} + O(q^{100}) \)

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.l.a 475.l 19.e $6$ $3.793$ \(\Q(\zeta_{18})\) None \(6\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots\)
475.2.l.b 475.l 19.e $18$ $3.793$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{14}q^{2}+(\beta _{4}-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+\cdots\)
475.2.l.c 475.l 19.e $18$ $3.793$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{4}-\beta _{15})q^{2}+(-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
475.2.l.d 475.l 19.e $42$ $3.793$ None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
475.2.l.e 475.l 19.e $42$ $3.793$ None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
475.2.l.f 475.l 19.e $48$ $3.793$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$

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

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