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Properties

Label 418.2.j
Level $418$
Weight $2$
Character orbit 418.j
Rep. character $\chi_{418}(23,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $108$
Newform subspaces $4$
Sturm bound $120$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.j (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(418, [\chi])\).

Total New Old
Modular forms 384 108 276
Cusp forms 336 108 228
Eisenstein series 48 0 48

Trace form

\( 108 q + O(q^{10}) \) \( 108 q - 24 q^{13} + 60 q^{15} + 12 q^{17} + 48 q^{18} - 36 q^{19} - 48 q^{21} + 24 q^{23} + 24 q^{25} + 12 q^{28} + 24 q^{29} - 6 q^{31} + 12 q^{34} + 12 q^{35} + 6 q^{38} + 24 q^{39} - 24 q^{41} + 12 q^{42} - 12 q^{43} - 36 q^{45} - 78 q^{49} - 72 q^{51} + 12 q^{52} - 96 q^{53} - 72 q^{54} - 48 q^{56} + 60 q^{57} + 84 q^{59} - 12 q^{60} + 72 q^{61} - 72 q^{62} - 24 q^{63} - 54 q^{64} - 60 q^{65} + 48 q^{69} + 72 q^{70} - 42 q^{71} + 60 q^{73} + 24 q^{74} + 36 q^{78} - 12 q^{79} - 48 q^{81} + 24 q^{82} + 36 q^{83} - 36 q^{84} + 48 q^{85} - 30 q^{86} + 84 q^{87} + 6 q^{88} - 18 q^{89} - 120 q^{90} - 96 q^{91} - 12 q^{92} + 96 q^{93} - 48 q^{95} - 90 q^{97} + 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(418, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
418.2.j.a 418.j 19.e $24$ $3.338$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
418.2.j.b 418.j 19.e $24$ $3.338$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$
418.2.j.c 418.j 19.e $30$ $3.338$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{9}]$
418.2.j.d 418.j 19.e $30$ $3.338$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(418, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(418, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)