Properties

Label 10.5.c
Level 10
Weight 5
Character orbit c
Rep. character \(\chi_{10}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 2
Sturm bound 7
Trace bound 2

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 10.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\(4q \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut -\mathstrut 60q^{5} \) \(\mathstrut -\mathstrut 64q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 20q^{3} \) \(\mathstrut -\mathstrut 60q^{5} \) \(\mathstrut -\mathstrut 64q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 160q^{10} \) \(\mathstrut +\mathstrut 168q^{11} \) \(\mathstrut +\mathstrut 160q^{12} \) \(\mathstrut -\mathstrut 60q^{13} \) \(\mathstrut +\mathstrut 20q^{15} \) \(\mathstrut -\mathstrut 256q^{16} \) \(\mathstrut -\mathstrut 1020q^{17} \) \(\mathstrut -\mathstrut 640q^{18} \) \(\mathstrut +\mathstrut 968q^{21} \) \(\mathstrut +\mathstrut 1280q^{22} \) \(\mathstrut +\mathstrut 1620q^{23} \) \(\mathstrut -\mathstrut 700q^{25} \) \(\mathstrut -\mathstrut 1344q^{26} \) \(\mathstrut +\mathstrut 320q^{27} \) \(\mathstrut -\mathstrut 160q^{28} \) \(\mathstrut +\mathstrut 960q^{30} \) \(\mathstrut -\mathstrut 1112q^{31} \) \(\mathstrut -\mathstrut 1720q^{33} \) \(\mathstrut -\mathstrut 2220q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 1020q^{37} \) \(\mathstrut +\mathstrut 960q^{38} \) \(\mathstrut +\mathstrut 1280q^{40} \) \(\mathstrut +\mathstrut 5448q^{41} \) \(\mathstrut -\mathstrut 2240q^{42} \) \(\mathstrut +\mathstrut 660q^{43} \) \(\mathstrut +\mathstrut 6400q^{45} \) \(\mathstrut +\mathstrut 2176q^{46} \) \(\mathstrut +\mathstrut 1620q^{47} \) \(\mathstrut -\mathstrut 1280q^{48} \) \(\mathstrut -\mathstrut 4800q^{50} \) \(\mathstrut -\mathstrut 10712q^{51} \) \(\mathstrut -\mathstrut 480q^{52} \) \(\mathstrut -\mathstrut 4860q^{53} \) \(\mathstrut -\mathstrut 2520q^{55} \) \(\mathstrut +\mathstrut 3072q^{56} \) \(\mathstrut +\mathstrut 5120q^{57} \) \(\mathstrut +\mathstrut 3520q^{58} \) \(\mathstrut -\mathstrut 4960q^{60} \) \(\mathstrut -\mathstrut 7032q^{61} \) \(\mathstrut -\mathstrut 3840q^{62} \) \(\mathstrut +\mathstrut 7700q^{63} \) \(\mathstrut +\mathstrut 7620q^{65} \) \(\mathstrut +\mathstrut 10112q^{66} \) \(\mathstrut +\mathstrut 8660q^{67} \) \(\mathstrut +\mathstrut 8160q^{68} \) \(\mathstrut +\mathstrut 1600q^{70} \) \(\mathstrut +\mathstrut 5928q^{71} \) \(\mathstrut -\mathstrut 5120q^{72} \) \(\mathstrut -\mathstrut 12860q^{73} \) \(\mathstrut -\mathstrut 13100q^{75} \) \(\mathstrut -\mathstrut 5120q^{76} \) \(\mathstrut -\mathstrut 14520q^{77} \) \(\mathstrut -\mathstrut 5760q^{78} \) \(\mathstrut +\mathstrut 3840q^{80} \) \(\mathstrut +\mathstrut 964q^{81} \) \(\mathstrut -\mathstrut 2560q^{82} \) \(\mathstrut -\mathstrut 300q^{83} \) \(\mathstrut +\mathstrut 16580q^{85} \) \(\mathstrut -\mathstrut 14784q^{86} \) \(\mathstrut +\mathstrut 11840q^{87} \) \(\mathstrut -\mathstrut 10240q^{88} \) \(\mathstrut +\mathstrut 9440q^{90} \) \(\mathstrut +\mathstrut 15528q^{91} \) \(\mathstrut +\mathstrut 12960q^{92} \) \(\mathstrut +\mathstrut 2120q^{93} \) \(\mathstrut -\mathstrut 9600q^{95} \) \(\mathstrut +\mathstrut 4096q^{96} \) \(\mathstrut -\mathstrut 13500q^{97} \) \(\mathstrut +\mathstrut 3840q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.5.c.a \(2\) \(1.034\) \(\Q(\sqrt{-1}) \) None \(-4\) \(18\) \(-30\) \(58\) \(q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots\)
10.5.c.b \(2\) \(1.034\) \(\Q(\sqrt{-1}) \) None \(4\) \(2\) \(-30\) \(-38\) \(q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)