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

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

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

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