Properties

Label 507.2.b
Level $507$
Weight $2$
Character orbit 507.b
Rep. character $\chi_{507}(337,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $7$
Sturm bound $121$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(121\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(507, [\chi])\).

Total New Old
Modular forms 74 26 48
Cusp forms 46 26 20
Eisenstein series 28 0 28

Trace form

\( 26q + 2q^{3} - 26q^{4} + 26q^{9} + O(q^{10}) \) \( 26q + 2q^{3} - 26q^{4} + 26q^{9} + 4q^{10} + 2q^{12} - 16q^{14} + 34q^{16} + 16q^{17} - 20q^{22} + 4q^{23} - 34q^{25} + 2q^{27} - 20q^{29} + 4q^{30} - 4q^{35} - 26q^{36} + 16q^{38} - 12q^{40} + 12q^{42} + 20q^{43} - 18q^{48} - 10q^{49} - 8q^{51} - 28q^{53} - 12q^{55} - 12q^{61} + 4q^{62} - 6q^{64} + 8q^{66} - 36q^{68} + 4q^{69} + 12q^{74} + 18q^{75} + 40q^{77} + 4q^{79} + 26q^{81} - 4q^{82} + 8q^{87} + 12q^{88} + 4q^{90} - 28q^{92} + 20q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(507, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
507.2.b.a \(2\) \(4.048\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
507.2.b.b \(2\) \(4.048\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}+q^{4}-iq^{5}-iq^{6}-2iq^{7}+\cdots\)
507.2.b.c \(2\) \(4.048\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+2q^{4}+2\zeta_{6}q^{5}-\zeta_{6}q^{7}+q^{9}+\cdots\)
507.2.b.d \(4\) \(4.048\) \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
507.2.b.e \(4\) \(4.048\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+q^{3}+(-1-\zeta_{8}^{3})q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
507.2.b.f \(6\) \(4.048\) 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}-q^{3}+(-3-\beta _{2}+\cdots)q^{4}+\cdots\)
507.2.b.g \(6\) \(4.048\) 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(507, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)