Properties

Label 335.2.e
Level 335
Weight 2
Character orbit e
Rep. character \(\chi_{335}(96,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 44
Newforms 2
Sturm bound 68
Trace bound 1

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Defining parameters

Level: \( N \) = \( 335 = 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 335.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
Sturm bound: \(68\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(335, [\chi])\).

Total New Old
Modular forms 72 44 28
Cusp forms 64 44 20
Eisenstein series 8 0 8

Trace form

\(44q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(44q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 44q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 24q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 64q^{24} \) \(\mathstrut +\mathstrut 44q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 42q^{32} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 18q^{38} \) \(\mathstrut -\mathstrut 38q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut +\mathstrut 40q^{42} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 16q^{44} \) \(\mathstrut +\mathstrut 30q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 36q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 70q^{57} \) \(\mathstrut -\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 28q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 88q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 76q^{68} \) \(\mathstrut +\mathstrut 10q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut +\mathstrut 144q^{72} \) \(\mathstrut +\mathstrut 50q^{73} \) \(\mathstrut +\mathstrut 32q^{74} \) \(\mathstrut -\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 92q^{81} \) \(\mathstrut -\mathstrut 32q^{82} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 40q^{84} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut +\mathstrut 132q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 64q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 46q^{93} \) \(\mathstrut +\mathstrut 44q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut -\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 42q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(335, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
335.2.e.a \(20\) \(2.675\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(0\) \(-20\) \(-4\) \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(\beta _{10}-\beta _{18})q^{4}+\cdots\)
335.2.e.b \(24\) \(2.675\) None \(-3\) \(0\) \(24\) \(-2\)

Decomposition of \(S_{2}^{\mathrm{old}}(335, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(335, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)