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

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

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

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