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Properties

Label 15.5.f
Level $15$
Weight $5$
Character orbit 15.f
Rep. character $\chi_{15}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $1$
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: \(\Q(i)\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.5.f.a 15.f 5.c $8$ $1.551$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-84\) \(20\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)

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

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