Properties

Label 950.2.bc
Level $950$
Weight $2$
Character orbit 950.bc
Rep. character $\chi_{950}(61,\cdot)$
Character field $\Q(\zeta_{45})$
Dimension $1200$
Newform subspaces $2$
Sturm bound $300$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bc (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{45})\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 3696 1200 2496
Cusp forms 3504 1200 2304
Eisenstein series 192 0 192

Trace form

\( 1200q + 12q^{7} + O(q^{10}) \) \( 1200q + 12q^{7} - 18q^{11} - 54q^{15} + 36q^{17} + 48q^{18} - 12q^{20} - 36q^{22} - 12q^{23} + 120q^{25} - 36q^{29} - 108q^{33} + 6q^{35} + 216q^{43} + 84q^{45} + 60q^{46} - 36q^{47} - 540q^{49} - 24q^{50} - 120q^{51} + 36q^{53} + 36q^{54} - 108q^{55} - 48q^{56} - 108q^{57} - 36q^{59} + 6q^{60} + 144q^{61} + 24q^{62} + 36q^{63} + 150q^{64} + 120q^{65} - 96q^{66} + 12q^{68} + 48q^{69} + 12q^{70} + 120q^{71} + 36q^{73} - 48q^{77} - 48q^{79} + 96q^{81} - 48q^{82} - 54q^{83} + 78q^{84} - 96q^{85} - 60q^{87} - 72q^{89} - 36q^{90} - 84q^{92} - 84q^{93} - 96q^{94} + 156q^{97} + 216q^{98} - 192q^{99} + O(q^{100}) \)

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.bc.a \(600\) \(7.586\) None \(0\) \(0\) \(0\) \(-42\)
950.2.bc.b \(600\) \(7.586\) None \(0\) \(0\) \(0\) \(54\)

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

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