Properties

Label 950.2.e
Level $950$
Weight $2$
Character orbit 950.e
Rep. character $\chi_{950}(201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $66$
Newform subspaces $15$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
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 66 258
Cusp forms 276 66 210
Eisenstein series 48 0 48

Trace form

\( 66q - q^{2} - q^{3} - 33q^{4} + q^{6} - 12q^{7} + 2q^{8} - 36q^{9} + O(q^{10}) \) \( 66q - q^{2} - q^{3} - 33q^{4} + q^{6} - 12q^{7} + 2q^{8} - 36q^{9} - 2q^{11} + 2q^{12} + 10q^{13} - 2q^{14} - 33q^{16} - 2q^{17} - 12q^{18} + 25q^{19} + 26q^{21} - q^{22} - 8q^{23} + q^{24} - 12q^{26} + 14q^{27} + 6q^{28} + 6q^{29} - 16q^{31} - q^{32} - 9q^{33} + 2q^{34} - 36q^{36} + 8q^{37} + 12q^{38} - 52q^{39} + 25q^{41} + 14q^{42} + 12q^{43} + q^{44} - 24q^{46} + 22q^{47} - q^{48} + 42q^{49} - 16q^{51} + 10q^{52} + 2q^{53} - 29q^{54} + 4q^{56} - 16q^{57} - 4q^{58} + 35q^{59} + 10q^{61} + 8q^{63} + 66q^{64} - 9q^{66} + 19q^{67} + 4q^{68} + 8q^{69} + 2q^{71} + 6q^{72} + 27q^{73} + 4q^{74} - 17q^{76} + 52q^{77} + 2q^{78} - 69q^{81} - 9q^{82} - 10q^{83} - 52q^{84} - 16q^{86} - 28q^{87} + 2q^{88} + 34q^{89} - 32q^{91} - 8q^{92} - 40q^{93} - 52q^{94} - 2q^{96} - 27q^{97} - 17q^{98} - 36q^{99} + O(q^{100}) \)

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.e.a \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.b \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.c \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(8\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{7}+q^{8}+\cdots\)
950.2.e.d \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(8\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.e \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-8\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}-q^{8}+\cdots\)
950.2.e.f \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}+3\zeta_{6}q^{9}+\cdots\)
950.2.e.g \(2\) \(7.586\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(4\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.h \(4\) \(7.586\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-1\) \(0\) \(-10\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.i \(4\) \(7.586\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-2\) \(1\) \(0\) \(-4\) \(q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.j \(4\) \(7.586\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(2\) \(-1\) \(0\) \(4\) \(q+(1+\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.k \(4\) \(7.586\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(0\) \(-4\) \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.l \(8\) \(7.586\) 8.0.\(\cdots\).1 None \(-4\) \(1\) \(0\) \(12\) \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.m \(8\) \(7.586\) 8.0.\(\cdots\).1 None \(4\) \(-1\) \(0\) \(-12\) \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.n \(10\) \(7.586\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(0\) \(0\) \(-10\) \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.o \(10\) \(7.586\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(5\) \(0\) \(0\) \(10\) \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)