Properties

Label 380.3.m
Level $380$
Weight $3$
Character orbit 380.m
Rep. character $\chi_{380}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $36$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
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 252 36 216
Cusp forms 228 36 192
Eisenstein series 24 0 24

Trace form

\( 36 q - 4 q^{3} + 10 q^{5} + 22 q^{7} + O(q^{10}) \) \( 36 q - 4 q^{3} + 10 q^{5} + 22 q^{7} - 24 q^{11} - 28 q^{13} - 16 q^{15} - 26 q^{17} + 104 q^{21} + 20 q^{23} - 18 q^{25} + 20 q^{27} - 56 q^{31} - 16 q^{33} - 110 q^{35} - 4 q^{37} + 120 q^{41} - 10 q^{43} - 168 q^{45} + 38 q^{47} - 24 q^{51} + 128 q^{53} + 136 q^{55} + 40 q^{61} + 34 q^{63} + 224 q^{65} + 220 q^{67} - 360 q^{71} - 66 q^{73} + 16 q^{75} - 62 q^{77} - 284 q^{81} + 556 q^{83} + 276 q^{85} - 72 q^{87} - 40 q^{91} - 200 q^{93} - 38 q^{95} - 376 q^{97} + O(q^{100}) \)

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.m.a 380.m 5.c $36$ $10.354$ None \(0\) \(-4\) \(10\) \(22\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{3}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)