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 $3$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.5.c.a \(1\) \(3.618\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(-17\) \(25\) \(49\) \(q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots\)
35.5.c.b \(1\) \(3.618\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(17\) \(-25\) \(-49\) \(q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots\)
35.5.c.c \(2\) \(3.618\) \(\Q(\sqrt{-6}) \) None \(0\) \(-10\) \(-10\) \(-70\) \(q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots\)
35.5.c.d \(2\) \(3.618\) \(\Q(\sqrt{-6}) \) None \(0\) \(10\) \(10\) \(70\) \(q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots\)
35.5.c.e \(8\) \(3.618\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots\)