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Properties

Label 465.2.be
Level $465$
Weight $2$
Character orbit 465.be
Rep. character $\chi_{465}(98,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{12})\)
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 272 272 0
Cusp forms 240 240 0
Eisenstein series 32 32 0

Trace form

\( 240 q - 6 q^{3} - 4 q^{6} + O(q^{10}) \) \( 240 q - 6 q^{3} - 4 q^{6} + 4 q^{10} + 24 q^{12} - 4 q^{13} - 24 q^{15} - 216 q^{16} - 6 q^{18} - 4 q^{21} + 8 q^{22} + 48 q^{27} + 16 q^{28} + 60 q^{30} - 24 q^{31} - 4 q^{33} + 12 q^{36} + 12 q^{40} + 70 q^{42} - 4 q^{43} + 38 q^{45} - 96 q^{46} + 48 q^{48} + 4 q^{51} + 20 q^{52} - 52 q^{55} - 34 q^{57} - 104 q^{58} - 96 q^{60} + 16 q^{61} - 64 q^{63} - 208 q^{66} + 8 q^{67} + 96 q^{70} + 64 q^{72} + 12 q^{73} - 12 q^{75} - 12 q^{76} + 76 q^{78} + 12 q^{81} + 52 q^{82} - 56 q^{85} + 22 q^{87} + 48 q^{88} - 80 q^{91} + 6 q^{93} - 68 q^{96} - 144 q^{97} + O(q^{100}) \)

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.be.a 465.be 465.ae $240$ $3.713$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$