Properties

Label 15.8.e
Level 15
Weight 8
Character orbit e
Rep. character \(\chi_{15}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 24
Newforms 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 15.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(15, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 24 24 0
Eisenstein series 8 8 0

Trace form

\( 24q + 24q^{3} + 924q^{6} + 1344q^{7} + O(q^{10}) \) \( 24q + 24q^{3} + 924q^{6} + 1344q^{7} - 3180q^{10} - 2028q^{12} + 16848q^{13} + 37560q^{15} - 68868q^{16} - 106560q^{18} + 84144q^{21} + 166020q^{22} - 275760q^{25} - 264168q^{27} + 602028q^{28} + 892380q^{30} - 208992q^{31} - 877800q^{33} - 256212q^{36} - 635616q^{37} - 1574040q^{40} + 1219380q^{42} + 1397328q^{43} + 570240q^{45} + 2787168q^{46} - 476796q^{48} - 4028016q^{51} - 6426336q^{52} + 2324880q^{55} + 8457264q^{57} + 986340q^{58} + 2037900q^{60} + 12157968q^{61} - 1973952q^{63} - 25406040q^{66} - 16720176q^{67} - 13165860q^{70} + 36245880q^{72} + 4059528q^{73} + 11226120q^{75} + 37968816q^{76} - 26156280q^{78} - 31289976q^{81} - 53633520q^{82} - 34181760q^{85} + 44480160q^{87} + 74717340q^{88} + 71623080q^{90} + 67599648q^{91} - 58742592q^{93} - 103105308q^{96} - 75148056q^{97} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.8.e.a \(24\) \(4.686\) None \(0\) \(24\) \(0\) \(1344\)