Properties

Label 5.10.b
Level 5
Weight 10
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(5, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 1368q^{4} \) \(\mathstrut +\mathstrut 1140q^{5} \) \(\mathstrut +\mathstrut 2808q^{6} \) \(\mathstrut +\mathstrut 11628q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 1368q^{4} \) \(\mathstrut +\mathstrut 1140q^{5} \) \(\mathstrut +\mathstrut 2808q^{6} \) \(\mathstrut +\mathstrut 11628q^{9} \) \(\mathstrut -\mathstrut 69160q^{10} \) \(\mathstrut +\mathstrut 109968q^{11} \) \(\mathstrut -\mathstrut 424536q^{14} \) \(\mathstrut -\mathstrut 396720q^{15} \) \(\mathstrut +\mathstrut 1631264q^{16} \) \(\mathstrut -\mathstrut 636880q^{19} \) \(\mathstrut -\mathstrut 3302280q^{20} \) \(\mathstrut +\mathstrut 3523968q^{21} \) \(\mathstrut -\mathstrut 2435040q^{24} \) \(\mathstrut -\mathstrut 1337900q^{25} \) \(\mathstrut +\mathstrut 6618768q^{26} \) \(\mathstrut -\mathstrut 3531720q^{29} \) \(\mathstrut +\mathstrut 3712680q^{30} \) \(\mathstrut -\mathstrut 10587712q^{31} \) \(\mathstrut +\mathstrut 26434624q^{34} \) \(\mathstrut +\mathstrut 13629840q^{35} \) \(\mathstrut -\mathstrut 56399976q^{36} \) \(\mathstrut +\mathstrut 1686816q^{39} \) \(\mathstrut +\mathstrut 43578400q^{40} \) \(\mathstrut -\mathstrut 16788552q^{41} \) \(\mathstrut +\mathstrut 20638944q^{44} \) \(\mathstrut +\mathstrut 55737180q^{45} \) \(\mathstrut -\mathstrut 61250072q^{46} \) \(\mathstrut -\mathstrut 46921028q^{49} \) \(\mathstrut -\mathstrut 150092400q^{50} \) \(\mathstrut +\mathstrut 84017088q^{51} \) \(\mathstrut +\mathstrut 115855920q^{54} \) \(\mathstrut -\mathstrut 26907120q^{55} \) \(\mathstrut +\mathstrut 315178080q^{56} \) \(\mathstrut -\mathstrut 460829040q^{59} \) \(\mathstrut -\mathstrut 307006560q^{60} \) \(\mathstrut +\mathstrut 360490568q^{61} \) \(\mathstrut +\mathstrut 134995072q^{64} \) \(\mathstrut +\mathstrut 183895680q^{65} \) \(\mathstrut +\mathstrut 18949536q^{66} \) \(\mathstrut -\mathstrut 286524864q^{69} \) \(\mathstrut -\mathstrut 508341960q^{70} \) \(\mathstrut -\mathstrut 47611872q^{71} \) \(\mathstrut +\mathstrut 1176861744q^{74} \) \(\mathstrut +\mathstrut 659239200q^{75} \) \(\mathstrut -\mathstrut 1168489440q^{76} \) \(\mathstrut -\mathstrut 728043520q^{79} \) \(\mathstrut +\mathstrut 965843040q^{80} \) \(\mathstrut -\mathstrut 343387836q^{81} \) \(\mathstrut +\mathstrut 1118898144q^{84} \) \(\mathstrut +\mathstrut 1275419840q^{85} \) \(\mathstrut -\mathstrut 2375904552q^{86} \) \(\mathstrut -\mathstrut 1582700760q^{89} \) \(\mathstrut -\mathstrut 1197088920q^{90} \) \(\mathstrut +\mathstrut 473322528q^{91} \) \(\mathstrut +\mathstrut 3327101704q^{94} \) \(\mathstrut +\mathstrut 1204791600q^{95} \) \(\mathstrut +\mathstrut 399339648q^{96} \) \(\mathstrut -\mathstrut 728787024q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.10.b.a \(4\) \(2.575\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(1140\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots\)