Properties

Label 35.5.d
Level $35$
Weight $5$
Character orbit 35.d
Rep. character $\chi_{35}(6,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 18 12 6
Cusp forms 14 12 2
Eisenstein series 4 0 4

Trace form

\( 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9} + 126 q^{11} + 78 q^{14} + 50 q^{15} + 578 q^{16} + 734 q^{18} - 642 q^{21} + 2264 q^{22} - 756 q^{23} - 1500 q^{25} + 1414 q^{28} - 2190 q^{29} + 1600 q^{30} - 8682 q^{32} - 150 q^{35} - 3582 q^{36} + 5564 q^{37} + 8634 q^{39} + 5580 q^{42} + 3944 q^{43} - 11196 q^{44} + 7844 q^{46} - 8796 q^{49} + 750 q^{50} + 7206 q^{51} + 11760 q^{53} - 6606 q^{56} - 12900 q^{57} - 18496 q^{58} - 11700 q^{60} - 4310 q^{63} + 20146 q^{64} - 750 q^{65} - 24096 q^{67} + 14400 q^{70} - 5664 q^{71} + 39214 q^{72} + 17604 q^{74} + 26904 q^{77} + 20100 q^{78} - 1590 q^{79} - 11912 q^{81} - 43128 q^{84} + 1050 q^{85} + 17604 q^{86} - 7268 q^{88} - 7182 q^{91} - 60252 q^{92} - 70980 q^{93} - 3000 q^{95} + 57714 q^{98} + 23084 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.5.d.a 35.d 7.b $12$ $3.618$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(-50\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)