Properties

Label 462.2.a
Level $462$
Weight $2$
Character orbit 462.a
Rep. character $\chi_{462}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $8$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(462))\).

Total New Old
Modular forms 104 9 95
Cusp forms 89 9 80
Eisenstein series 15 0 15

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

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(6\)

Trace form

\( 9q - 3q^{2} + q^{3} + 9q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + 9q^{9} + O(q^{10}) \) \( 9q - 3q^{2} + q^{3} + 9q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + 9q^{9} - 2q^{10} + q^{11} + q^{12} + 6q^{13} + q^{14} + 6q^{15} + 9q^{16} - 6q^{17} - 3q^{18} + 4q^{19} - 2q^{20} + q^{21} - 3q^{22} - 16q^{23} + q^{24} + 7q^{25} - 18q^{26} + q^{27} + q^{28} - 26q^{29} + 6q^{30} + 24q^{31} - 3q^{32} + q^{33} - 6q^{34} - 10q^{35} + 9q^{36} + 6q^{37} - 4q^{38} + 14q^{39} - 2q^{40} - 14q^{41} - 3q^{42} + 4q^{43} + q^{44} - 2q^{45} + 8q^{47} + q^{48} + 9q^{49} + 3q^{50} + 10q^{51} + 6q^{52} - 2q^{53} + q^{54} + 6q^{55} + q^{56} + 20q^{57} - 2q^{58} - 4q^{59} + 6q^{60} - 10q^{61} + q^{63} + 9q^{64} + 20q^{65} + q^{66} + 20q^{67} - 6q^{68} + 8q^{69} - 2q^{70} - 16q^{71} - 3q^{72} - 14q^{73} - 18q^{74} - q^{75} + 4q^{76} + q^{77} - 2q^{78} - 48q^{79} - 2q^{80} + 9q^{81} + 18q^{82} - 12q^{83} + q^{84} + 12q^{85} + 4q^{86} - 2q^{87} - 3q^{88} - 38q^{89} - 2q^{90} - 2q^{91} - 16q^{92} - 8q^{93} - 24q^{95} + q^{96} - 14q^{97} - 3q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(462))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 11
462.2.a.a \(1\) \(3.689\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
462.2.a.b \(1\) \(3.689\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.c \(1\) \(3.689\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.d \(1\) \(3.689\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.e \(1\) \(3.689\) \(\Q\) None \(1\) \(-1\) \(-4\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{7}+\cdots\)
462.2.a.f \(1\) \(3.689\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
462.2.a.g \(1\) \(3.689\) \(\Q\) None \(1\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.h \(2\) \(3.689\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(462))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(462)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)