Properties

Label 950.2.n
Level $950$
Weight $2$
Character orbit 950.n
Rep. character $\chi_{950}(39,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $184$
Newform subspaces $2$
Sturm bound $300$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 616 184 432
Cusp forms 584 184 400
Eisenstein series 32 0 32

Trace form

\( 184q + 46q^{4} + 18q^{5} - 4q^{6} + 58q^{9} + O(q^{10}) \) \( 184q + 46q^{4} + 18q^{5} - 4q^{6} + 58q^{9} + 2q^{11} + 20q^{12} + 4q^{15} - 46q^{16} - 10q^{17} + 2q^{19} + 2q^{20} + 10q^{23} - 16q^{24} - 54q^{25} + 56q^{26} - 60q^{27} - 20q^{28} - 8q^{29} + 12q^{30} - 12q^{31} + 100q^{33} - 6q^{35} - 58q^{36} + 20q^{37} + 40q^{39} + 44q^{41} + 20q^{42} + 8q^{44} - 26q^{45} + 20q^{48} - 188q^{49} - 8q^{50} - 24q^{51} - 40q^{53} + 16q^{54} - 12q^{59} - 4q^{60} - 16q^{61} - 50q^{63} + 46q^{64} - 12q^{65} - 16q^{66} + 60q^{67} - 16q^{69} + 16q^{70} + 40q^{71} - 80q^{73} - 72q^{74} + 84q^{75} + 8q^{76} - 100q^{78} - 16q^{79} - 2q^{80} + 14q^{81} - 150q^{83} + 82q^{85} - 24q^{86} + 20q^{88} - 88q^{89} - 72q^{90} + 16q^{91} - 20q^{92} + 2q^{95} - 4q^{96} - 20q^{97} - 28q^{99} + O(q^{100}) \)

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.n.a \(88\) \(7.586\) None \(0\) \(0\) \(10\) \(0\)
950.2.n.b \(96\) \(7.586\) None \(0\) \(0\) \(8\) \(0\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)