↑

Properties

Label 380.3.bc
Level $380$
Weight $3$
Character orbit 380.bc
Rep. character $\chi_{380}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $120$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 380.bc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
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 756 120 636
Cusp forms 684 120 564
Eisenstein series 72 0 72

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 30 q^{11} - 3 q^{15} + 24 q^{19} - 72 q^{21} + 150 q^{25} + 60 q^{29} + 171 q^{35} + 24 q^{39} - 12 q^{41} - 90 q^{45} + 270 q^{49} - 144 q^{51} + 3 q^{55} + 84 q^{59} + 396 q^{61} - 405 q^{65} + 420 q^{71} + 96 q^{79} - 120 q^{81} + 30 q^{85} + 12 q^{89} - 84 q^{91} + 267 q^{95} + 324 q^{99} + O(q^{100}) \)

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.bc.a 380.bc 95.o $120$ $10.354$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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