Properties

Label 35.3.c
Level $35$
Weight $3$
Character orbit 35.c
Rep. character $\chi_{35}(34,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $12$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6q - 12q^{4} - 12q^{9} + O(q^{10}) \) \( 6q - 12q^{4} - 12q^{9} + 30q^{11} + 36q^{14} - 30q^{15} - 12q^{16} - 66q^{21} - 30q^{25} + 102q^{29} + 180q^{30} - 30q^{35} - 84q^{36} - 78q^{39} - 384q^{44} + 144q^{46} + 222q^{49} - 180q^{50} + 138q^{51} - 36q^{56} + 60q^{60} + 492q^{64} + 210q^{65} - 360q^{70} - 60q^{71} - 216q^{74} - 618q^{79} - 246q^{81} + 456q^{84} - 330q^{85} + 504q^{86} - 186q^{91} + 540q^{95} + 264q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.3.c.a \(1\) \(0.954\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(-1\) \(5\) \(-7\) \(q-q^{3}+4q^{4}+5q^{5}-7q^{7}-8q^{9}+\cdots\)
35.3.c.b \(1\) \(0.954\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(1\) \(-5\) \(7\) \(q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\cdots\)
35.3.c.c \(4\) \(0.954\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-5q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)