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Properties

Label 403.3.t
Level $403$
Weight $3$
Character orbit 403.t
Rep. character $\chi_{403}(30,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 403.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(403, [\chi])\).

Total New Old
Modular forms 152 152 0
Cusp forms 144 144 0
Eisenstein series 8 8 0

Trace form

\( 144 q - 6 q^{2} + 134 q^{4} - 48 q^{7} + 196 q^{9} + O(q^{10}) \) \( 144 q - 6 q^{2} + 134 q^{4} - 48 q^{7} + 196 q^{9} + 6 q^{10} - 56 q^{14} - 258 q^{16} - 48 q^{19} + 210 q^{20} - 632 q^{25} - 270 q^{28} - 366 q^{32} + 330 q^{33} + 98 q^{35} - 158 q^{36} - 412 q^{38} + 234 q^{39} + 420 q^{40} + 120 q^{41} + 114 q^{45} + 288 q^{49} - 264 q^{50} - 224 q^{51} - 150 q^{56} + 102 q^{59} + 26 q^{62} - 474 q^{63} - 1036 q^{64} + 552 q^{66} + 48 q^{67} - 232 q^{69} + 306 q^{71} + 102 q^{72} + 144 q^{76} + 546 q^{78} + 984 q^{80} - 504 q^{81} + 172 q^{82} + 360 q^{87} + 1632 q^{90} - 192 q^{93} + 728 q^{94} - 72 q^{95} + 1260 q^{97} + 402 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(403, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
403.3.t.a 403.t 403.t $144$ $10.981$ None \(-6\) \(0\) \(0\) \(-48\) $\mathrm{SU}(2)[C_{6}]$