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 $3$

Related objects

Downloads

Learn more about

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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 31
465.2.a.a \(1\) \(3.713\) \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
465.2.a.b \(1\) \(3.713\) \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
465.2.a.c \(2\) \(3.713\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
465.2.a.d \(2\) \(3.713\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-6\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+(-3+\cdots)q^{7}+\cdots\)
465.2.a.e \(3\) \(3.713\) 3.3.564.1 None \(1\) \(-3\) \(-3\) \(8\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
465.2.a.f \(3\) \(3.713\) 3.3.148.1 None \(1\) \(3\) \(3\) \(2\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
465.2.a.g \(3\) \(3.713\) 3.3.148.1 None \(3\) \(3\) \(-3\) \(2\) \(-\) \(+\) \(+\) \(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
465.2.a.h \(4\) \(3.713\) 4.4.8468.1 None \(2\) \(-4\) \(4\) \(4\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)

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

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