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

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

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
950.2.bc.a 950.bc 475.ac $600$ $7.586$ None \(0\) \(0\) \(0\) \(-42\) $\mathrm{SU}(2)[C_{45}]$
950.2.bc.b 950.bc 475.ac $600$ $7.586$ None \(0\) \(0\) \(0\) \(54\) $\mathrm{SU}(2)[C_{45}]$

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

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