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Properties

Label 403.2.h
Level $403$
Weight $2$
Character orbit 403.h
Rep. character $\chi_{403}(118,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 80 64 16
Cusp forms 72 64 8
Eisenstein series 8 0 8

Trace form

\( 64 q - 4 q^{3} + 56 q^{4} + 2 q^{5} + 4 q^{7} + 12 q^{8} - 36 q^{9} + O(q^{10}) \) \( 64 q - 4 q^{3} + 56 q^{4} + 2 q^{5} + 4 q^{7} + 12 q^{8} - 36 q^{9} - 10 q^{10} - 8 q^{11} - 16 q^{12} - 2 q^{13} - 4 q^{14} + 12 q^{15} + 40 q^{16} - 4 q^{17} + 8 q^{19} + 2 q^{20} - 2 q^{21} + 14 q^{22} - 20 q^{23} - 12 q^{24} - 46 q^{25} - 6 q^{26} + 32 q^{27} + 6 q^{28} + 8 q^{29} - 32 q^{30} + 10 q^{31} - 16 q^{32} - 12 q^{33} - 36 q^{34} + 20 q^{35} - 12 q^{36} - 10 q^{37} - 2 q^{38} - 46 q^{40} + 2 q^{41} + 52 q^{42} + 14 q^{43} - 92 q^{44} + 28 q^{45} - 24 q^{46} - 8 q^{47} - 18 q^{48} - 26 q^{49} + 2 q^{50} - 10 q^{51} - 6 q^{52} + 34 q^{53} + 32 q^{54} + 34 q^{55} - 48 q^{56} + 8 q^{57} - 12 q^{58} + 18 q^{59} + 40 q^{60} - 20 q^{61} - 42 q^{62} - 24 q^{63} + 116 q^{64} - 12 q^{65} + 200 q^{66} - 2 q^{67} + 2 q^{68} - 18 q^{69} - 56 q^{70} + 30 q^{71} - 18 q^{72} - 20 q^{73} - 14 q^{74} - 20 q^{75} + 8 q^{76} + 4 q^{77} - 14 q^{79} - 22 q^{80} - 40 q^{81} - 48 q^{82} - 10 q^{83} - 10 q^{84} + 76 q^{85} - 34 q^{86} + 22 q^{88} + 32 q^{89} + 42 q^{90} + 16 q^{91} - 92 q^{92} - 4 q^{93} - 84 q^{94} - 128 q^{96} - 52 q^{97} + 12 q^{98} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.h.a 403.h 31.c $30$ $3.218$ None \(-6\) \(-2\) \(7\) \(6\) $\mathrm{SU}(2)[C_{3}]$
403.2.h.b 403.h 31.c $34$ $3.218$ None \(6\) \(-2\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(403, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(403, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)