Properties

Label 950.2.b
Level $950$
Weight $2$
Character orbit 950.b
Rep. character $\chi_{950}(799,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $8$
Sturm bound $300$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(300\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 162 26 136
Cusp forms 138 26 112
Eisenstein series 24 0 24

Trace form

\( 26q - 26q^{4} + 4q^{6} - 38q^{9} + O(q^{10}) \) \( 26q - 26q^{4} + 4q^{6} - 38q^{9} + 8q^{11} - 8q^{14} + 26q^{16} + 2q^{19} + 32q^{21} - 4q^{24} - 24q^{26} - 28q^{29} + 4q^{34} + 38q^{36} - 8q^{39} - 12q^{41} - 8q^{44} + 40q^{46} - 62q^{49} + 40q^{51} - 16q^{54} + 8q^{56} - 24q^{59} + 36q^{61} - 26q^{64} + 56q^{69} + 8q^{71} + 48q^{74} - 2q^{76} - 48q^{79} + 42q^{81} - 32q^{84} + 52q^{89} - 24q^{91} - 56q^{94} + 4q^{96} + 32q^{99} + O(q^{100}) \)

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.b.a \(2\) \(7.586\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-5iq^{7}+\cdots\)
950.2.b.b \(2\) \(7.586\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
950.2.b.c \(2\) \(7.586\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
950.2.b.d \(2\) \(7.586\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
950.2.b.e \(2\) \(7.586\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
950.2.b.f \(4\) \(7.586\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
950.2.b.g \(6\) \(7.586\) 6.0.4227136.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4})q^{3}-q^{4}+\cdots\)
950.2.b.h \(6\) \(7.586\) 6.0.63107136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)