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Properties

Label 380.2.u
Level $380$
Weight $2$
Character orbit 380.u
Rep. character $\chi_{380}(61,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $36$
Newform subspaces $2$
Sturm bound $120$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 396 36 360
Cusp forms 324 36 288
Eisenstein series 72 0 72

Trace form

\( 36 q + 6 q^{3} + 6 q^{9} + O(q^{10}) \) \( 36 q + 6 q^{3} + 6 q^{9} + 18 q^{13} + 24 q^{17} + 6 q^{21} + 12 q^{23} + 18 q^{27} - 42 q^{29} - 12 q^{31} - 12 q^{33} + 6 q^{35} + 24 q^{37} - 96 q^{39} - 12 q^{41} + 6 q^{43} + 6 q^{47} - 18 q^{49} - 18 q^{51} + 60 q^{53} + 42 q^{57} + 48 q^{59} - 24 q^{61} - 18 q^{63} + 18 q^{65} + 24 q^{67} + 18 q^{69} - 36 q^{71} - 42 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 6 q^{81} - 36 q^{83} + 12 q^{87} + 12 q^{89} - 48 q^{93} - 36 q^{97} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.u.a 380.u 19.e $18$ $3.034$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{3}-\beta _{7})q^{3}-\beta _{4}q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
380.2.u.b 380.u 19.e $18$ $3.034$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{13}q^{3}+(\beta _{2}-\beta _{11})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)