Properties

Label 507.2.k
Level $507$
Weight $2$
Character orbit 507.k
Rep. character $\chi_{507}(80,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $164$
Newform subspaces $11$
Sturm bound $121$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 11 \)
Sturm bound: \(121\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 300 244 56
Cusp forms 188 164 24
Eisenstein series 112 80 32

Trace form

\( 164q + 2q^{3} + 12q^{4} + 2q^{6} + 14q^{7} + 2q^{9} + O(q^{10}) \) \( 164q + 2q^{3} + 12q^{4} + 2q^{6} + 14q^{7} + 2q^{9} - 12q^{10} + 14q^{15} + 4q^{16} - 4q^{18} + 2q^{19} - 22q^{21} - 12q^{22} - 18q^{24} - 76q^{27} - 18q^{30} + 6q^{31} - 16q^{33} + 36q^{34} + 36q^{36} + 30q^{37} - 56q^{40} + 24q^{42} - 30q^{43} + 20q^{45} + 106q^{48} - 18q^{49} - 46q^{54} + 4q^{55} - 28q^{57} - 28q^{58} - 44q^{60} - 36q^{61} - 16q^{63} + 8q^{67} + 32q^{70} - 12q^{72} + 62q^{73} + 18q^{75} + 36q^{76} - 112q^{79} + 14q^{81} + 24q^{82} + 8q^{84} - 12q^{85} - 22q^{87} + 12q^{88} - 10q^{93} - 112q^{94} - 16q^{96} + 18q^{97} - 40q^{99} + O(q^{100}) \)

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.k.a \(4\) \(4.048\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-8\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(-1+\cdots)q^{7}+\cdots\)
507.2.k.b \(4\) \(4.048\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(8\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(1+\zeta_{12}+\cdots)q^{7}+\cdots\)
507.2.k.c \(4\) \(4.048\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(10\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(2+\cdots)q^{7}+\cdots\)
507.2.k.d \(8\) \(4.048\) 8.0.56070144.2 None \(0\) \(-2\) \(0\) \(4\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+2\beta _{5}+\beta _{7})q^{2}+\cdots\)
507.2.k.e \(8\) \(4.048\) 8.0.56070144.2 None \(0\) \(-2\) \(0\) \(-4\) \(q+(\beta _{2}-\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}+\beta _{4})q^{3}+\cdots\)
507.2.k.f \(8\) \(4.048\) 8.0.56070144.2 None \(0\) \(-2\) \(0\) \(4\) \(q+(\beta _{2}-\beta _{5}-\beta _{7})q^{2}+(\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
507.2.k.g \(8\) \(4.048\) 8.0.56070144.2 \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-\beta _{2}-2\beta _{3})q^{3}+(-2+2\beta _{3}+\cdots)q^{4}+\cdots\)
507.2.k.h \(8\) \(4.048\) 8.0.56070144.2 \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(2\beta _{2}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)
507.2.k.i \(8\) \(4.048\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(0\) \(4\) \(q+\zeta_{24}^{7}q^{2}+(\zeta_{24}+\zeta_{24}^{4}-\zeta_{24}^{7})q^{3}+\cdots\)
507.2.k.j \(8\) \(4.048\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(0\) \(-4\) \(q+\zeta_{24}^{7}q^{2}+(-\zeta_{24}+\zeta_{24}^{4}+\zeta_{24}^{7})q^{3}+\cdots\)
507.2.k.k \(96\) \(4.048\) None \(0\) \(0\) \(0\) \(0\)

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

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