Properties

Label 10.9.c
Level 10
Weight 9
Character orbit c
Rep. character \(\chi_{10}(3,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 2
Sturm bound 13
Trace bound 2

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 9 \)
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: \(13\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(10, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

Trace form

\(8q \) \(\mathstrut +\mathstrut 140q^{3} \) \(\mathstrut -\mathstrut 780q^{5} \) \(\mathstrut +\mathstrut 512q^{6} \) \(\mathstrut +\mathstrut 4540q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 140q^{3} \) \(\mathstrut -\mathstrut 780q^{5} \) \(\mathstrut +\mathstrut 512q^{6} \) \(\mathstrut +\mathstrut 4540q^{7} \) \(\mathstrut -\mathstrut 6400q^{10} \) \(\mathstrut -\mathstrut 34584q^{11} \) \(\mathstrut +\mathstrut 17920q^{12} \) \(\mathstrut +\mathstrut 119280q^{13} \) \(\mathstrut -\mathstrut 252580q^{15} \) \(\mathstrut -\mathstrut 131072q^{16} \) \(\mathstrut +\mathstrut 202560q^{17} \) \(\mathstrut +\mathstrut 158720q^{18} \) \(\mathstrut +\mathstrut 53760q^{20} \) \(\mathstrut +\mathstrut 110696q^{21} \) \(\mathstrut +\mathstrut 40960q^{22} \) \(\mathstrut +\mathstrut 174540q^{23} \) \(\mathstrut -\mathstrut 368000q^{25} \) \(\mathstrut -\mathstrut 450048q^{26} \) \(\mathstrut -\mathstrut 704560q^{27} \) \(\mathstrut -\mathstrut 581120q^{28} \) \(\mathstrut +\mathstrut 1697280q^{30} \) \(\mathstrut +\mathstrut 2342456q^{31} \) \(\mathstrut -\mathstrut 3190840q^{33} \) \(\mathstrut +\mathstrut 4359900q^{35} \) \(\mathstrut -\mathstrut 618496q^{36} \) \(\mathstrut -\mathstrut 6531240q^{37} \) \(\mathstrut -\mathstrut 5076480q^{38} \) \(\mathstrut +\mathstrut 1146880q^{40} \) \(\mathstrut +\mathstrut 6454056q^{41} \) \(\mathstrut +\mathstrut 13150720q^{42} \) \(\mathstrut +\mathstrut 12059820q^{43} \) \(\mathstrut -\mathstrut 14797820q^{45} \) \(\mathstrut -\mathstrut 17410048q^{46} \) \(\mathstrut -\mathstrut 8748660q^{47} \) \(\mathstrut -\mathstrut 2293760q^{48} \) \(\mathstrut +\mathstrut 5414400q^{50} \) \(\mathstrut +\mathstrut 4713976q^{51} \) \(\mathstrut +\mathstrut 15267840q^{52} \) \(\mathstrut +\mathstrut 30279480q^{53} \) \(\mathstrut -\mathstrut 31155960q^{55} \) \(\mathstrut -\mathstrut 14155776q^{56} \) \(\mathstrut -\mathstrut 21729760q^{57} \) \(\mathstrut -\mathstrut 24194560q^{58} \) \(\mathstrut +\mathstrut 18675200q^{60} \) \(\mathstrut +\mathstrut 41805096q^{61} \) \(\mathstrut +\mathstrut 56017920q^{62} \) \(\mathstrut +\mathstrut 21701900q^{63} \) \(\mathstrut -\mathstrut 18428280q^{65} \) \(\mathstrut -\mathstrut 94667776q^{66} \) \(\mathstrut -\mathstrut 47676980q^{67} \) \(\mathstrut -\mathstrut 25927680q^{68} \) \(\mathstrut +\mathstrut 105582080q^{70} \) \(\mathstrut +\mathstrut 133410936q^{71} \) \(\mathstrut +\mathstrut 20316160q^{72} \) \(\mathstrut -\mathstrut 72484120q^{73} \) \(\mathstrut +\mathstrut 1104700q^{75} \) \(\mathstrut -\mathstrut 44615680q^{76} \) \(\mathstrut -\mathstrut 200406840q^{77} \) \(\mathstrut -\mathstrut 100792320q^{78} \) \(\mathstrut +\mathstrut 12779520q^{80} \) \(\mathstrut +\mathstrut 131272288q^{81} \) \(\mathstrut +\mathstrut 120186880q^{82} \) \(\mathstrut +\mathstrut 135315900q^{83} \) \(\mathstrut -\mathstrut 3822800q^{85} \) \(\mathstrut -\mathstrut 35731968q^{86} \) \(\mathstrut +\mathstrut 66654080q^{87} \) \(\mathstrut -\mathstrut 5242880q^{88} \) \(\mathstrut -\mathstrut 21256960q^{90} \) \(\mathstrut -\mathstrut 291657384q^{91} \) \(\mathstrut +\mathstrut 22341120q^{92} \) \(\mathstrut +\mathstrut 115691240q^{93} \) \(\mathstrut -\mathstrut 242319600q^{95} \) \(\mathstrut -\mathstrut 8388608q^{96} \) \(\mathstrut +\mathstrut 173745000q^{97} \) \(\mathstrut +\mathstrut 115169280q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(10, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.9.c.a \(4\) \(4.074\) \(\Q(i, \sqrt{249})\) None \(-32\) \(54\) \(90\) \(-1186\) \(q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.9.c.b \(4\) \(4.074\) \(\Q(i, \sqrt{601})\) None \(32\) \(86\) \(-870\) \(5726\) \(q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)