Properties

Label 403.2.i
Level $403$
Weight $2$
Character orbit 403.i
Rep. character $\chi_{403}(216,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $1$
Sturm bound $74$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(74\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

Total New Old
Modular forms 76 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

Trace form

\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} + O(q^{10}) \) \( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
403.2.i.a 403.i 403.i $68$ $3.218$ None \(-4\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{4}]$