Properties

Label 35.4.f
Level $35$
Weight $4$
Character orbit 35.f
Rep. character $\chi_{35}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(35, [\chi])\).

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

Trace form

\( 20 q - 4 q^{2} - 10 q^{7} + 112 q^{8} + O(q^{10}) \) \( 20 q - 4 q^{2} - 10 q^{7} + 112 q^{8} - 56 q^{11} - 340 q^{15} - 248 q^{16} + 152 q^{18} + 468 q^{21} + 156 q^{22} - 308 q^{23} - 300 q^{25} - 528 q^{28} + 1460 q^{30} + 432 q^{32} + 90 q^{35} + 344 q^{36} + 116 q^{37} - 1580 q^{42} + 572 q^{43} - 912 q^{46} - 700 q^{50} - 944 q^{51} + 1420 q^{53} + 2648 q^{56} - 3200 q^{57} - 4348 q^{58} - 2000 q^{60} + 1830 q^{63} + 1660 q^{65} + 3396 q^{67} - 1020 q^{70} + 2704 q^{71} + 8936 q^{72} - 4024 q^{77} + 6860 q^{78} - 3164 q^{81} - 1460 q^{85} - 12872 q^{86} - 3584 q^{88} + 4268 q^{91} - 6328 q^{92} - 4480 q^{93} + 3400 q^{95} + 4092 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.4.f.a 35.f 35.f $4$ $2.065$ \(\Q(i, \sqrt{5})\) None 35.4.f.a \(-8\) \(0\) \(0\) \(-42\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2})q^{3}+\cdots\)
35.4.f.b 35.f 35.f $16$ $2.065$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 35.4.f.b \(4\) \(0\) \(0\) \(32\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{2}-\beta _{8}q^{3}+(-4\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)