Properties

Label 402.2.e
Level 402
Weight 2
Character orbit e
Rep. character \(\chi_{402}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 24
Newforms 4
Sturm bound 136
Trace bound 3

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Defining parameters

Level: \( N \) = \( 402 = 2 \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 402.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 4 \)
Sturm bound: \(136\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(402, [\chi])\).

Total New Old
Modular forms 144 24 120
Cusp forms 128 24 104
Eisenstein series 16 0 16

Trace form

\( 24q - 12q^{4} + 24q^{9} + O(q^{10}) \) \( 24q - 12q^{4} + 24q^{9} - 4q^{11} + 8q^{13} + 8q^{14} + 8q^{15} - 12q^{16} - 4q^{17} + 8q^{19} - 4q^{21} - 16q^{22} + 12q^{23} + 40q^{25} + 16q^{29} + 4q^{30} + 28q^{31} - 4q^{33} + 4q^{34} - 28q^{35} - 12q^{36} - 12q^{37} + 12q^{39} - 12q^{41} - 8q^{42} + 8q^{43} - 4q^{44} + 44q^{47} - 24q^{49} - 16q^{50} - 8q^{51} - 16q^{52} + 8q^{53} - 12q^{55} - 4q^{56} - 8q^{57} - 16q^{58} - 24q^{59} - 4q^{60} - 12q^{61} - 40q^{62} + 24q^{64} + 12q^{65} - 24q^{66} - 44q^{67} + 8q^{68} - 8q^{69} + 8q^{70} - 44q^{71} - 12q^{73} + 12q^{74} - 16q^{75} - 16q^{76} - 20q^{77} + 16q^{78} - 36q^{79} + 24q^{81} + 12q^{83} - 4q^{84} - 12q^{85} + 32q^{86} + 8q^{88} + 48q^{89} + 56q^{91} - 24q^{92} + 8q^{93} - 64q^{94} - 4q^{95} - 4q^{97} + 16q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(402, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
402.2.e.a \(6\) \(3.210\) 6.0.16638075.1 None \(-3\) \(-6\) \(0\) \(-1\) \(q+\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
402.2.e.b \(6\) \(3.210\) 6.0.48843675.1 None \(-3\) \(6\) \(0\) \(-1\) \(q+(-1+\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}-\beta _{2}q^{5}+\cdots\)
402.2.e.c \(6\) \(3.210\) 6.0.309123.1 None \(3\) \(-6\) \(-4\) \(3\) \(q+\beta _{4}q^{2}-q^{3}+(-1+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
402.2.e.d \(6\) \(3.210\) 6.0.18825075.4 None \(3\) \(6\) \(4\) \(-1\) \(q-\beta _{1}q^{2}+q^{3}+(-1-\beta _{1})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(402, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(402, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 2}\)