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Properties

Label 380.3.x
Level $380$
Weight $3$
Character orbit 380.x
Rep. character $\chi_{380}(197,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 380.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(380, [\chi])\).

Total New Old
Modular forms 504 80 424
Cusp forms 456 80 376
Eisenstein series 48 0 48

Trace form

\( 80 q + 2 q^{5} - 12 q^{7} + O(q^{10}) \) \( 80 q + 2 q^{5} - 12 q^{7} - 16 q^{11} - 8 q^{13} - 6 q^{15} - 32 q^{17} + 24 q^{21} - 60 q^{23} - 50 q^{25} - 84 q^{27} + 112 q^{31} + 12 q^{33} + 76 q^{35} - 128 q^{37} - 40 q^{41} + 58 q^{43} - 116 q^{45} + 70 q^{47} - 8 q^{51} - 82 q^{53} - 136 q^{55} + 322 q^{57} + 104 q^{61} - 86 q^{63} + 280 q^{65} - 72 q^{67} - 32 q^{71} - 292 q^{73} + 108 q^{75} + 420 q^{77} + 336 q^{81} - 100 q^{83} - 296 q^{85} + 200 q^{87} + 112 q^{91} + 16 q^{93} - 308 q^{95} - 122 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.3.x.a 380.x 95.m $80$ $10.354$ None \(0\) \(0\) \(2\) \(-12\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

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