↑

Properties

Label 465.2.br
Level $465$
Weight $2$
Character orbit 465.br
Rep. character $\chi_{465}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $336$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(465, [\chi])\).

Total New Old
Modular forms 544 336 208
Cusp forms 480 336 144
Eisenstein series 64 0 64

Trace form

\( 336 q + 76 q^{4} - 18 q^{6} + O(q^{10}) \) \( 336 q + 76 q^{4} - 18 q^{6} - 2 q^{10} - 30 q^{12} + 18 q^{13} - 80 q^{16} - 10 q^{18} - 30 q^{19} + 42 q^{21} + 36 q^{24} + 168 q^{25} + 30 q^{27} - 132 q^{28} - 12 q^{31} + 34 q^{33} - 22 q^{34} - 6 q^{36} - 18 q^{37} - 32 q^{39} - 64 q^{40} - 20 q^{42} + 68 q^{43} - 4 q^{45} + 50 q^{46} - 108 q^{48} + 62 q^{49} - 32 q^{51} - 144 q^{52} - 220 q^{54} - 8 q^{55} - 168 q^{57} - 140 q^{58} - 88 q^{63} + 20 q^{64} + 116 q^{66} + 32 q^{67} - 264 q^{69} - 136 q^{72} + 10 q^{73} + 56 q^{76} - 56 q^{78} + 30 q^{79} + 172 q^{81} + 236 q^{82} + 100 q^{84} - 34 q^{87} + 72 q^{88} - 48 q^{90} + 30 q^{91} + 150 q^{93} - 160 q^{94} + 142 q^{96} - 22 q^{97} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(465, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
465.2.br.a 465.br 93.p $336$ $3.713$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(465, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)