Properties

Label 465.2.a
Level $465$
Weight $2$
Character orbit 465.a
Rep. character $\chi_{465}(1,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $8$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(128\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(465))\).

Total New Old
Modular forms 68 19 49
Cusp forms 61 19 42
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(13\)

Trace form

\( 19 q + 5 q^{2} - q^{3} + 21 q^{4} - q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + O(q^{10}) \) \( 19 q + 5 q^{2} - q^{3} + 21 q^{4} - q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + q^{10} + 12 q^{11} - 7 q^{12} - 14 q^{13} - 8 q^{14} - q^{15} + 13 q^{16} - 10 q^{17} + 5 q^{18} - 4 q^{19} - 7 q^{20} - 8 q^{21} + 4 q^{22} + 9 q^{24} + 19 q^{25} + 6 q^{26} - q^{27} + 32 q^{28} + 10 q^{29} - 3 q^{30} - q^{31} + 33 q^{32} - 4 q^{33} - 14 q^{34} + 21 q^{36} + 18 q^{37} - 20 q^{38} - 14 q^{39} - 3 q^{40} - 10 q^{41} + 16 q^{42} - 20 q^{43} - 12 q^{44} - q^{45} + 24 q^{46} - 16 q^{47} + q^{48} + 27 q^{49} + 5 q^{50} - 10 q^{51} - 42 q^{52} + 2 q^{53} - 3 q^{54} - 4 q^{55} - 32 q^{56} - 20 q^{57} - 26 q^{58} - 20 q^{59} - 7 q^{60} - 38 q^{61} - 3 q^{62} - 3 q^{64} + 18 q^{65} + 20 q^{66} - 12 q^{67} - 54 q^{68} + 8 q^{69} + 8 q^{70} + 32 q^{71} + 9 q^{72} - 34 q^{73} - 42 q^{74} - q^{75} + 4 q^{76} - 10 q^{78} + 16 q^{79} + q^{80} + 19 q^{81} - 38 q^{82} + 36 q^{83} - 32 q^{84} - 18 q^{85} + 20 q^{86} + 18 q^{87} + 4 q^{88} + 6 q^{89} + q^{90} + 32 q^{91} - 32 q^{92} + 3 q^{93} - 32 q^{94} + 12 q^{95} - 15 q^{96} - 18 q^{97} - 3 q^{98} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(465))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 31
465.2.a.a 465.a 1.a $1$ $3.713$ \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
465.2.a.b 465.a 1.a $1$ $3.713$ \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
465.2.a.c 465.a 1.a $2$ $3.713$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
465.2.a.d 465.a 1.a $2$ $3.713$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+(-3+\cdots)q^{7}+\cdots\)
465.2.a.e 465.a 1.a $3$ $3.713$ 3.3.564.1 None \(1\) \(-3\) \(-3\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
465.2.a.f 465.a 1.a $3$ $3.713$ 3.3.148.1 None \(1\) \(3\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
465.2.a.g 465.a 1.a $3$ $3.713$ 3.3.148.1 None \(3\) \(3\) \(-3\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
465.2.a.h 465.a 1.a $4$ $3.713$ 4.4.8468.1 None \(2\) \(-4\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(465))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(465)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 2}\)