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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.3.d.a 35.d 7.b $2$ $0.954$ \(\Q(\sqrt{-5}) \) None 35.3.d.a \(-2\) \(0\) \(0\) \(14\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
35.3.d.b 35.d 7.b $2$ $0.954$ \(\Q(\sqrt{-5}) \) None 35.3.d.b \(4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)

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

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