Properties

Label 510.2.f
Level 510
Weight 2
Character orbit f
Rep. character \(\chi_{510}(169,\cdot)\)
Character field \(\Q\)
Dimension 20
Newform subspaces 4
Sturm bound 216
Trace bound 3

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Defining parameters

Level: \( N \) = \( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 510.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 85 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(216\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(510, [\chi])\).

Total New Old
Modular forms 116 20 96
Cusp forms 100 20 80
Eisenstein series 16 0 16

Trace form

\( 20q - 20q^{4} + 20q^{9} + O(q^{10}) \) \( 20q - 20q^{4} + 20q^{9} - 4q^{15} + 20q^{16} + 16q^{19} + 8q^{21} - 4q^{25} - 16q^{26} + 8q^{30} - 4q^{34} - 8q^{35} - 20q^{36} + 20q^{49} - 8q^{50} + 8q^{51} + 16q^{55} + 32q^{59} + 4q^{60} - 20q^{64} - 24q^{66} - 40q^{69} - 48q^{70} - 16q^{76} + 20q^{81} - 8q^{84} - 32q^{85} + 8q^{86} - 88q^{89} - 16q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(510, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
510.2.f.a \(4\) \(4.072\) \(\Q(i, \sqrt{6})\) None \(0\) \(-4\) \(4\) \(-8\) \(q+\beta _{2}q^{2}-q^{3}-q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
510.2.f.b \(4\) \(4.072\) \(\Q(i, \sqrt{6})\) None \(0\) \(4\) \(-4\) \(8\) \(q+\beta _{2}q^{2}+q^{3}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
510.2.f.c \(6\) \(4.072\) 6.0.350464.1 None \(0\) \(-6\) \(-2\) \(4\) \(q+\beta _{4}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
510.2.f.d \(6\) \(4.072\) 6.0.350464.1 None \(0\) \(6\) \(2\) \(-4\) \(q-\beta _{4}q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(510, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(510, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)