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Properties

Label 950.2.h
Level $950$
Weight $2$
Character orbit 950.h
Rep. character $\chi_{950}(191,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $176$
Newform subspaces $5$
Sturm bound $300$
Trace bound $5$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 616 176 440
Cusp forms 584 176 408
Eisenstein series 32 0 32

Trace form

\( 176 q + 2 q^{2} + 8 q^{3} - 44 q^{4} - 12 q^{5} + 4 q^{6} + 12 q^{7} + 2 q^{8} - 32 q^{9} + O(q^{10}) \) \( 176 q + 2 q^{2} + 8 q^{3} - 44 q^{4} - 12 q^{5} + 4 q^{6} + 12 q^{7} + 2 q^{8} - 32 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 12 q^{13} + 12 q^{15} - 44 q^{16} - 2 q^{17} - 40 q^{18} + 2 q^{19} - 2 q^{20} + 8 q^{22} + 2 q^{23} - 16 q^{24} - 36 q^{25} - 36 q^{26} - 4 q^{27} - 8 q^{28} + 12 q^{29} + 12 q^{30} + 12 q^{31} - 8 q^{32} - 44 q^{33} - 30 q^{34} + 38 q^{35} - 32 q^{36} + 30 q^{37} + 40 q^{39} + 10 q^{40} - 24 q^{41} + 12 q^{42} + 20 q^{43} + 8 q^{44} + 60 q^{45} + 36 q^{47} - 12 q^{48} + 172 q^{49} + 10 q^{50} + 24 q^{51} + 12 q^{52} + 18 q^{53} + 16 q^{54} + 56 q^{55} + 60 q^{58} - 12 q^{59} - 28 q^{60} + 36 q^{61} - 72 q^{62} - 2 q^{63} - 44 q^{64} + 54 q^{65} + 16 q^{66} - 4 q^{67} + 8 q^{68} - 136 q^{69} - 112 q^{70} + 40 q^{71} + 10 q^{72} - 8 q^{73} - 52 q^{74} - 20 q^{75} - 8 q^{76} + 56 q^{77} - 60 q^{78} - 16 q^{79} + 8 q^{80} - 24 q^{81} - 92 q^{82} - 50 q^{83} - 36 q^{85} + 24 q^{86} + 56 q^{87} - 12 q^{88} - 38 q^{89} + 10 q^{90} - 16 q^{91} - 8 q^{92} + 64 q^{93} + 2 q^{95} + 4 q^{96} + 120 q^{97} + 18 q^{98} + 52 q^{99} + O(q^{100}) \)

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.h.a 950.h 25.d $4$ $7.586$ \(\Q(\zeta_{10})\) None \(1\) \(4\) \(5\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots\)
950.2.h.b 950.h 25.d $40$ $7.586$ None \(-10\) \(5\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{5}]$
950.2.h.c 950.h 25.d $44$ $7.586$ None \(-11\) \(1\) \(-1\) \(18\) $\mathrm{SU}(2)[C_{5}]$
950.2.h.d 950.h 25.d $44$ $7.586$ None \(11\) \(-1\) \(-11\) \(-10\) $\mathrm{SU}(2)[C_{5}]$
950.2.h.e 950.h 25.d $44$ $7.586$ None \(11\) \(-1\) \(-5\) \(28\) $\mathrm{SU}(2)[C_{5}]$

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

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