Properties

Label 15.5.f
Level 15
Weight 5
Character orbit f
Rep. character \(\chi_{15}(7,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 15.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

Total New Old
Modular forms 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

Trace form

\(8q \) \(\mathstrut -\mathstrut 84q^{5} \) \(\mathstrut +\mathstrut 36q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 180q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 84q^{5} \) \(\mathstrut +\mathstrut 36q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 180q^{8} \) \(\mathstrut +\mathstrut 104q^{10} \) \(\mathstrut -\mathstrut 288q^{11} \) \(\mathstrut -\mathstrut 360q^{12} \) \(\mathstrut -\mathstrut 340q^{13} \) \(\mathstrut +\mathstrut 144q^{15} \) \(\mathstrut +\mathstrut 620q^{16} \) \(\mathstrut +\mathstrut 900q^{17} \) \(\mathstrut +\mathstrut 564q^{20} \) \(\mathstrut +\mathstrut 792q^{21} \) \(\mathstrut -\mathstrut 1100q^{22} \) \(\mathstrut -\mathstrut 1560q^{23} \) \(\mathstrut -\mathstrut 1204q^{25} \) \(\mathstrut -\mathstrut 3024q^{26} \) \(\mathstrut +\mathstrut 3580q^{28} \) \(\mathstrut -\mathstrut 2664q^{30} \) \(\mathstrut -\mathstrut 512q^{31} \) \(\mathstrut +\mathstrut 4980q^{32} \) \(\mathstrut +\mathstrut 2700q^{33} \) \(\mathstrut +\mathstrut 6600q^{35} \) \(\mathstrut +\mathstrut 2484q^{36} \) \(\mathstrut -\mathstrut 3820q^{37} \) \(\mathstrut -\mathstrut 7680q^{38} \) \(\mathstrut -\mathstrut 2952q^{40} \) \(\mathstrut -\mathstrut 2712q^{41} \) \(\mathstrut -\mathstrut 7380q^{42} \) \(\mathstrut -\mathstrut 1240q^{43} \) \(\mathstrut -\mathstrut 1944q^{45} \) \(\mathstrut +\mathstrut 13528q^{46} \) \(\mathstrut +\mathstrut 4800q^{47} \) \(\mathstrut +\mathstrut 3600q^{48} \) \(\mathstrut +\mathstrut 3744q^{50} \) \(\mathstrut +\mathstrut 6264q^{51} \) \(\mathstrut -\mathstrut 1240q^{52} \) \(\mathstrut +\mathstrut 1020q^{53} \) \(\mathstrut -\mathstrut 3644q^{55} \) \(\mathstrut -\mathstrut 30720q^{56} \) \(\mathstrut -\mathstrut 5400q^{57} \) \(\mathstrut +\mathstrut 2340q^{58} \) \(\mathstrut -\mathstrut 1044q^{60} \) \(\mathstrut -\mathstrut 4760q^{61} \) \(\mathstrut +\mathstrut 28680q^{62} \) \(\mathstrut +\mathstrut 540q^{63} \) \(\mathstrut -\mathstrut 1212q^{65} \) \(\mathstrut +\mathstrut 10008q^{66} \) \(\mathstrut -\mathstrut 8920q^{67} \) \(\mathstrut -\mathstrut 1920q^{68} \) \(\mathstrut +\mathstrut 7380q^{70} \) \(\mathstrut +\mathstrut 7536q^{71} \) \(\mathstrut -\mathstrut 4860q^{72} \) \(\mathstrut +\mathstrut 11600q^{73} \) \(\mathstrut -\mathstrut 5976q^{75} \) \(\mathstrut +\mathstrut 4344q^{76} \) \(\mathstrut -\mathstrut 360q^{77} \) \(\mathstrut -\mathstrut 4680q^{78} \) \(\mathstrut +\mathstrut 10644q^{80} \) \(\mathstrut -\mathstrut 5832q^{81} \) \(\mathstrut -\mathstrut 27200q^{82} \) \(\mathstrut -\mathstrut 32400q^{83} \) \(\mathstrut -\mathstrut 15628q^{85} \) \(\mathstrut +\mathstrut 14592q^{86} \) \(\mathstrut +\mathstrut 10620q^{87} \) \(\mathstrut -\mathstrut 14340q^{88} \) \(\mathstrut +\mathstrut 8964q^{90} \) \(\mathstrut +\mathstrut 16528q^{91} \) \(\mathstrut -\mathstrut 31800q^{92} \) \(\mathstrut +\mathstrut 14040q^{93} \) \(\mathstrut +\mathstrut 18864q^{95} \) \(\mathstrut -\mathstrut 4068q^{96} \) \(\mathstrut +\mathstrut 58640q^{97} \) \(\mathstrut +\mathstrut 46440q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.5.f.a \(8\) \(1.551\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-84\) \(20\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)