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 $0$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
465.2.br.a \(336\) \(3.713\) None \(0\) \(0\) \(0\) \(0\)

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

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