Properties

Label 35.3.d
Level $35$
Weight $3$
Character orbit 35.d
Rep. character $\chi_{35}(6,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $12$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\( 4q + 2q^{2} - 6q^{4} + 10q^{7} - 2q^{8} - 14q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 6q^{4} + 10q^{7} - 2q^{8} - 14q^{9} + 2q^{11} - 22q^{14} - 10q^{15} - 22q^{16} + 38q^{18} + 30q^{21} - 8q^{22} + 68q^{23} - 20q^{25} - 42q^{28} + 38q^{29} + 40q^{30} - 66q^{32} - 30q^{35} + 66q^{36} - 28q^{37} + 30q^{39} + 60q^{42} - 232q^{43} - 12q^{44} - 20q^{46} + 16q^{49} - 10q^{50} - 270q^{51} + 80q^{53} + 130q^{56} + 180q^{57} + 208q^{58} + 60q^{60} - 170q^{63} + 154q^{64} + 150q^{65} + 32q^{67} - 60q^{70} + 152q^{71} - 218q^{72} - 140q^{74} + 32q^{77} - 300q^{78} + 38q^{79} - 176q^{81} - 90q^{85} - 260q^{86} + 44q^{88} + 270q^{91} - 156q^{92} + 660q^{93} - 262q^{98} - 52q^{99} + O(q^{100}) \)

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.d.a \(2\) \(0.954\) \(\Q(\sqrt{-5}) \) None \(-2\) \(0\) \(0\) \(14\) \(q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
35.3.d.b \(2\) \(0.954\) \(\Q(\sqrt{-5}) \) None \(4\) \(0\) \(0\) \(-4\) \(q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)