Properties

Label 35.5.c
Level $35$
Weight $5$
Character orbit 35.c
Rep. character $\chi_{35}(34,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $5$
Sturm bound $20$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(20\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(35, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\( 14 q - 100 q^{4} + 264 q^{9} + O(q^{10}) \) \( 14 q - 100 q^{4} + 264 q^{9} - 166 q^{11} - 360 q^{14} - 690 q^{15} + 1124 q^{16} + 54 q^{21} + 2450 q^{25} - 1606 q^{29} - 3300 q^{30} - 1010 q^{35} + 2868 q^{36} + 5478 q^{39} - 880 q^{44} - 21576 q^{46} - 2830 q^{49} + 10140 q^{50} + 5598 q^{51} + 18564 q^{56} + 11580 q^{60} - 6724 q^{64} - 23890 q^{65} - 2220 q^{70} - 20356 q^{71} + 23736 q^{74} + 37954 q^{79} - 13518 q^{81} - 67056 q^{84} + 22450 q^{85} + 14304 q^{86} + 36034 q^{91} + 3660 q^{95} - 53688 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.5.c.a 35.c 35.c $1$ $3.618$ \(\Q\) \(\Q(\sqrt{-35}) \) 35.5.c.a \(0\) \(-17\) \(25\) \(49\) $\mathrm{U}(1)[D_{2}]$ \(q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots\)
35.5.c.b 35.c 35.c $1$ $3.618$ \(\Q\) \(\Q(\sqrt{-35}) \) 35.5.c.a \(0\) \(17\) \(-25\) \(-49\) $\mathrm{U}(1)[D_{2}]$ \(q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots\)
35.5.c.c 35.c 35.c $2$ $3.618$ \(\Q(\sqrt{-6}) \) None 35.5.c.c \(0\) \(-10\) \(-10\) \(-70\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots\)
35.5.c.d 35.c 35.c $2$ $3.618$ \(\Q(\sqrt{-6}) \) None 35.5.c.c \(0\) \(10\) \(10\) \(70\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots\)
35.5.c.e 35.c 35.c $8$ $3.618$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 35.5.c.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots\)