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Properties

Label 950.2.bd
Level $950$
Weight $2$
Character orbit 950.bd
Rep. character $\chi_{950}(27,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $800$
Newform subspaces $1$
Sturm bound $300$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(300\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 2464 800 1664
Cusp forms 2336 800 1536
Eisenstein series 128 0 128

Trace form

\( 800 q - 4 q^{5} - 8 q^{7} + O(q^{10}) \) \( 800 q - 4 q^{5} - 8 q^{7} - 36 q^{15} - 100 q^{16} - 4 q^{17} + 40 q^{19} - 96 q^{22} - 44 q^{23} - 4 q^{25} + 4 q^{28} + 120 q^{29} - 64 q^{30} + 132 q^{33} + 28 q^{35} + 100 q^{36} - 4 q^{38} - 80 q^{39} - 32 q^{42} - 36 q^{43} + 216 q^{45} + 76 q^{47} + 36 q^{53} + 88 q^{55} - 124 q^{57} + 120 q^{59} + 48 q^{60} - 8 q^{62} - 72 q^{63} - 24 q^{67} + 88 q^{68} + 24 q^{70} - 24 q^{73} - 256 q^{77} + 24 q^{78} + 4 q^{80} - 100 q^{81} - 8 q^{82} - 24 q^{83} + 28 q^{85} - 112 q^{87} - 12 q^{90} + 4 q^{92} - 108 q^{93} - 28 q^{95} + 12 q^{97} - 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bd.a 950.bd 475.ae $800$ $7.586$ None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{60}]$

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

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