Properties

Label 950.2.j
Level $950$
Weight $2$
Character orbit 950.j
Rep. character $\chi_{950}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $60$
Newform subspaces $9$
Sturm bound $300$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(300\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

Total New Old
Modular forms 324 60 264
Cusp forms 276 60 216
Eisenstein series 48 0 48

Trace form

\( 60q + 30q^{4} + 30q^{9} + O(q^{10}) \) \( 60q + 30q^{4} + 30q^{9} + 16q^{11} + 12q^{14} - 30q^{16} - 4q^{19} - 28q^{21} - 16q^{26} + 4q^{29} - 8q^{31} + 8q^{34} - 30q^{36} + 88q^{39} + 12q^{41} + 8q^{44} + 56q^{46} - 100q^{49} + 2q^{51} + 24q^{56} + 30q^{59} + 16q^{61} - 60q^{64} + 6q^{66} - 80q^{69} + 52q^{71} - 20q^{74} - 20q^{76} - 4q^{79} - 46q^{81} - 56q^{84} - 40q^{86} - 16q^{89} - 52q^{91} + 80q^{94} + 34q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
950.2.j.a \(4\) \(7.586\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.b \(4\) \(7.586\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.c \(4\) \(7.586\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+4\zeta_{12}^{3}q^{7}+\cdots\)
950.2.j.d \(4\) \(7.586\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
950.2.j.e \(4\) \(7.586\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.f \(8\) \(7.586\) 8.0.1731891456.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.j.g \(8\) \(7.586\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1+\beta _{3})q^{4}+\beta _{7}q^{6}+\cdots\)
950.2.j.h \(8\) \(7.586\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}+(1-\beta _{5})q^{4}+\cdots\)
950.2.j.i \(16\) \(7.586\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{14}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)