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Properties

Label 465.2.w
Level $465$
Weight $2$
Character orbit 465.w
Rep. character $\chi_{465}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $240$
Newform subspaces $3$
Sturm bound $128$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(2\)

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

\( 240 q - 64 q^{4} - 2 q^{9} + O(q^{10}) \) \( 240 q - 64 q^{4} - 2 q^{9} - 22 q^{10} - 15 q^{15} - 52 q^{16} + 8 q^{19} - 10 q^{21} + 30 q^{24} + 40 q^{31} - 40 q^{34} - 16 q^{36} + 2 q^{39} + 6 q^{40} - 42 q^{45} + 30 q^{46} - 20 q^{49} - 70 q^{51} - 10 q^{54} + 40 q^{55} + 65 q^{60} - 24 q^{64} - 124 q^{66} - 54 q^{69} - 52 q^{70} + 20 q^{75} - 98 q^{76} + 40 q^{79} + 26 q^{81} - 140 q^{84} - 20 q^{85} + 32 q^{90} - 40 q^{91} + 164 q^{94} + 90 q^{96} + O(q^{100}) \)

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.w.a 465.w 465.w $8$ $3.713$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(-1+\zeta_{15}-\zeta_{15}^{3}+2\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
465.2.w.b 465.w 465.w $8$ $3.713$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(1-\zeta_{15}+\zeta_{15}^{3}-2\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
465.2.w.c 465.w 465.w $224$ $3.713$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$