Properties

Label 15.12.e
Level $15$
Weight $12$
Character orbit 15.e
Rep. character $\chi_{15}(2,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 15.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(15, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 40 40 0
Eisenstein series 8 8 0

Trace form

\( 40 q + 504 q^{3} + 2940 q^{6} + 31504 q^{7} + O(q^{10}) \) \( 40 q + 504 q^{3} + 2940 q^{6} + 31504 q^{7} + 305140 q^{10} - 1714188 q^{12} - 3448472 q^{13} - 6075120 q^{15} - 43202180 q^{16} + 3729120 q^{18} + 33570840 q^{21} - 21743260 q^{22} - 68969000 q^{25} + 113282712 q^{27} + 253355948 q^{28} + 536094300 q^{30} + 67990880 q^{31} - 563443560 q^{33} + 1116103980 q^{36} + 1292573224 q^{37} - 2754089880 q^{40} - 5132304780 q^{42} + 4012128208 q^{43} + 4994447400 q^{45} - 8170829920 q^{46} - 13847034876 q^{48} + 5424535440 q^{51} + 10287332704 q^{52} - 23061806800 q^{55} - 10576855656 q^{57} + 56277468420 q^{58} + 66297294060 q^{60} - 24994982320 q^{61} - 50371112832 q^{63} + 56311074600 q^{66} + 37314988144 q^{67} - 90895488900 q^{70} - 92983114440 q^{72} + 51361482568 q^{73} + 96079968600 q^{75} - 121004023440 q^{76} - 104085843000 q^{78} - 22936122360 q^{81} - 56747065840 q^{82} + 5885083240 q^{85} + 84564024000 q^{87} + 148338843420 q^{88} + 17247857160 q^{90} + 230876677280 q^{91} + 38932525008 q^{93} - 437860137180 q^{96} - 294950050616 q^{97} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.12.e.a 15.e 15.e $40$ $11.525$ None \(0\) \(504\) \(0\) \(31504\) $\mathrm{SU}(2)[C_{4}]$