Properties

Label 403.2.k
Level 403
Weight 2
Character orbit k
Rep. character \(\chi_{403}(66,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 128
Newforms 5
Sturm bound 74
Trace bound 3

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 152 128 24
Cusp forms 136 128 8
Eisenstein series 16 0 16

Trace form

\( 128q - 4q^{3} - 40q^{4} - 4q^{5} + 8q^{6} + 12q^{7} - 6q^{8} - 36q^{9} + O(q^{10}) \) \( 128q - 4q^{3} - 40q^{4} - 4q^{5} + 8q^{6} + 12q^{7} - 6q^{8} - 36q^{9} - 22q^{10} - 8q^{11} - 16q^{12} - 2q^{13} - 26q^{15} - 16q^{16} + 6q^{17} + 24q^{19} - 22q^{20} - 20q^{21} - 8q^{22} - 10q^{23} + 4q^{24} + 72q^{25} + 24q^{26} + 38q^{27} - 30q^{28} + 4q^{29} - 68q^{30} + 24q^{31} + 8q^{32} + 2q^{33} - 48q^{34} - 32q^{35} + 40q^{36} + 40q^{37} - 42q^{38} - 12q^{40} - 8q^{41} + 26q^{42} - 28q^{43} + 18q^{44} + 44q^{45} + 8q^{46} + 36q^{47} + 16q^{48} + 22q^{49} - 66q^{50} + 26q^{51} - 6q^{52} - 10q^{53} + 42q^{54} - 28q^{55} - 48q^{56} + 2q^{58} + 24q^{59} - 50q^{60} - 28q^{61} + 4q^{62} - 60q^{63} - 20q^{64} - 2q^{65} + 2q^{66} + 68q^{67} + 16q^{68} - 28q^{69} + 4q^{70} + 186q^{72} - 22q^{74} + 12q^{75} - 110q^{76} - 4q^{77} - 68q^{79} + 60q^{80} - 42q^{81} + 52q^{82} - 36q^{83} + 40q^{84} - 40q^{85} - 12q^{86} - 40q^{87} + 64q^{88} - 58q^{89} - 110q^{90} - 8q^{91} - 32q^{92} + 76q^{93} + 112q^{94} + 18q^{95} - 68q^{96} - 46q^{97} - 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
403.2.k.a \(4\) \(3.218\) \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(-6\) \(-7\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-2\zeta_{10}+\cdots)q^{3}+\cdots\)
403.2.k.b \(4\) \(3.218\) \(\Q(\zeta_{10})\) None \(-1\) \(-2\) \(-4\) \(1\) \(q-\zeta_{10}q^{2}+(-2+2\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
403.2.k.c \(4\) \(3.218\) \(\Q(\zeta_{10})\) None \(-1\) \(3\) \(6\) \(-9\) \(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}^{3})q^{3}+\cdots\)
403.2.k.d \(48\) \(3.218\) None \(7\) \(-2\) \(-12\) \(25\)
403.2.k.e \(68\) \(3.218\) None \(-3\) \(-2\) \(12\) \(2\)

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

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