Properties

Label 950.2.r
Level $950$
Weight $2$
Character orbit 950.r
Rep. character $\chi_{950}(11,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $400$
Newform subspaces $2$
Sturm bound $300$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1232 400 832
Cusp forms 1168 400 768
Eisenstein series 64 0 64

Trace form

\( 400q + 50q^{4} + 2q^{5} - 8q^{7} + 50q^{9} + O(q^{10}) \) \( 400q + 50q^{4} + 2q^{5} - 8q^{7} + 50q^{9} + 12q^{11} + 16q^{13} + 8q^{14} + 6q^{15} + 50q^{16} - 18q^{17} - 32q^{18} - 12q^{19} - 4q^{20} + 32q^{21} + 12q^{22} - 2q^{23} + 10q^{25} - 36q^{27} + 4q^{28} + 24q^{29} - 12q^{30} + 8q^{34} - 20q^{35} + 50q^{36} + 16q^{37} + 20q^{38} - 24q^{39} + 16q^{41} + 32q^{42} + 60q^{43} + 4q^{44} + 8q^{45} + 32q^{46} - 44q^{47} + 360q^{49} - 8q^{50} - 52q^{51} + 16q^{52} - 36q^{53} - 12q^{54} - 16q^{56} + 108q^{57} + 48q^{59} - 14q^{60} + 28q^{61} - 8q^{62} - 66q^{63} - 100q^{64} + 216q^{65} - 16q^{66} - 72q^{67} - 104q^{68} - 16q^{69} - 16q^{70} + 14q^{71} + 16q^{72} - 40q^{73} - 80q^{75} + 8q^{76} - 128q^{77} - 60q^{78} - 8q^{79} + 2q^{80} - 6q^{81} - 8q^{82} - 56q^{83} + 56q^{84} - 10q^{85} + 20q^{86} - 176q^{87} + 16q^{88} + 12q^{89} - 114q^{90} + 8q^{91} + 8q^{92} - 132q^{93} - 32q^{95} + 2q^{97} + 16q^{98} - 12q^{99} + O(q^{100}) \)

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.r.a \(200\) \(7.586\) None \(-25\) \(0\) \(1\) \(-36\)
950.2.r.b \(200\) \(7.586\) None \(25\) \(0\) \(1\) \(28\)

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

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