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Properties

Label 15.7.f
Level $15$
Weight $7$
Character orbit 15.f
Rep. character $\chi_{15}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(15, [\chi])\).

Total New Old
Modular forms 28 12 16
Cusp forms 20 12 8
Eisenstein series 8 0 8

Trace form

\( 12 q + 16 q^{2} + 136 q^{5} + 324 q^{6} - 696 q^{7} - 3468 q^{8} + O(q^{10}) \) \( 12 q + 16 q^{2} + 136 q^{5} + 324 q^{6} - 696 q^{7} - 3468 q^{8} + 5304 q^{10} + 3248 q^{11} + 1944 q^{12} + 108 q^{13} - 4536 q^{15} - 16020 q^{16} - 5540 q^{17} + 3888 q^{18} + 12564 q^{20} - 15552 q^{21} + 49620 q^{22} + 11776 q^{23} - 65124 q^{25} + 24464 q^{26} + 23004 q^{28} + 17496 q^{30} + 10992 q^{31} - 126476 q^{32} - 17496 q^{33} - 59360 q^{35} + 61236 q^{36} - 105516 q^{37} - 55776 q^{38} + 376248 q^{40} + 395312 q^{41} + 143532 q^{42} + 7392 q^{43} + 32076 q^{45} - 751368 q^{46} - 246752 q^{47} - 423792 q^{48} - 669776 q^{50} - 225504 q^{51} + 694920 q^{52} + 954196 q^{53} - 74664 q^{55} + 961920 q^{56} + 412128 q^{57} - 324732 q^{58} + 705996 q^{60} - 420240 q^{61} - 1459672 q^{62} - 169128 q^{63} - 843212 q^{65} - 1180008 q^{66} + 1300800 q^{67} + 761696 q^{68} + 560820 q^{70} + 831584 q^{71} + 842724 q^{72} - 1208004 q^{73} + 769824 q^{75} - 292584 q^{76} - 3205552 q^{77} - 897480 q^{78} - 1124876 q^{80} - 708588 q^{81} + 815328 q^{82} + 1244224 q^{83} + 2746812 q^{85} + 8173568 q^{86} + 3063096 q^{87} - 948228 q^{88} - 32076 q^{90} - 5171328 q^{91} - 7092056 q^{92} - 1823472 q^{93} - 4466016 q^{95} - 5713092 q^{96} + 1506780 q^{97} + 6386552 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.7.f.a 15.f 5.c $12$ $3.451$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(16\) \(0\) \(136\) \(-696\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}-\beta _{4})q^{2}-\beta _{6}q^{3}+(18\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)