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Properties

Label 70.3.l
Level $70$
Weight $3$
Character orbit 70.l
Rep. character $\chi_{70}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $32$
Newform subspaces $3$
Sturm bound $36$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 70.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(70, [\chi])\).

Total New Old
Modular forms 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

Trace form

\( 32 q + 4 q^{5} - 16 q^{6} - 4 q^{7} + O(q^{10}) \) \( 32 q + 4 q^{5} - 16 q^{6} - 4 q^{7} - 16 q^{10} + 32 q^{11} - 72 q^{15} + 64 q^{16} + 92 q^{17} - 32 q^{18} - 24 q^{21} - 96 q^{22} + 72 q^{23} - 4 q^{25} - 32 q^{26} - 288 q^{27} - 64 q^{28} - 96 q^{30} - 248 q^{31} - 44 q^{33} + 232 q^{35} + 288 q^{36} - 28 q^{37} + 32 q^{38} + 112 q^{41} + 272 q^{42} + 280 q^{43} + 68 q^{45} + 72 q^{46} + 220 q^{47} - 192 q^{50} + 120 q^{51} + 204 q^{53} - 8 q^{55} - 112 q^{56} - 792 q^{57} + 160 q^{58} + 32 q^{60} - 528 q^{61} + 336 q^{62} - 256 q^{63} + 20 q^{65} - 80 q^{67} - 184 q^{68} + 144 q^{70} + 432 q^{71} - 64 q^{72} - 268 q^{73} + 464 q^{75} - 160 q^{76} + 676 q^{77} - 64 q^{78} - 16 q^{80} + 232 q^{81} + 128 q^{82} + 72 q^{83} - 128 q^{85} - 8 q^{86} + 388 q^{87} - 96 q^{88} - 1280 q^{90} - 864 q^{91} - 288 q^{92} - 132 q^{93} - 508 q^{95} - 32 q^{96} - 368 q^{97} - 224 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.3.l.a 70.l 35.l $8$ $1.907$ 8.0.3317760000.2 None \(4\) \(-4\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\beta _{2}-\beta _{4})q^{2}+(-\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
70.3.l.b 70.l 35.l $8$ $1.907$ 8.0.303595776.1 None \(4\) \(2\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\beta _{3}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
70.3.l.c 70.l 35.l $16$ $1.907$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(2\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\beta _{4}+\beta _{8})q^{2}+(-\beta _{3}-\beta _{10}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)