Properties

Label 462.4.a
Level $462$
Weight $4$
Character orbit 462.a
Rep. character $\chi_{462}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $19$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 462.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(462))\).

Total New Old
Modular forms 296 32 264
Cusp forms 280 32 248
Eisenstein series 16 0 16

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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(18\)
Minus space\(-\)\(14\)

Trace form

\( 32 q - 8 q^{2} + 128 q^{4} - 40 q^{5} - 32 q^{8} + 288 q^{9} + O(q^{10}) \) \( 32 q - 8 q^{2} + 128 q^{4} - 40 q^{5} - 32 q^{8} + 288 q^{9} - 80 q^{10} - 104 q^{13} + 512 q^{16} + 120 q^{17} - 72 q^{18} + 160 q^{19} - 160 q^{20} + 88 q^{22} + 472 q^{23} + 1056 q^{25} + 224 q^{26} - 280 q^{29} - 40 q^{31} - 128 q^{32} - 304 q^{34} - 224 q^{35} + 1152 q^{36} - 704 q^{37} + 336 q^{38} - 320 q^{40} + 344 q^{41} + 168 q^{42} + 248 q^{43} - 360 q^{45} + 400 q^{46} - 1256 q^{47} + 1568 q^{49} - 1400 q^{50} + 120 q^{51} - 416 q^{52} - 1624 q^{53} - 736 q^{58} + 976 q^{59} - 472 q^{61} + 128 q^{62} + 2048 q^{64} - 1424 q^{65} + 1824 q^{67} + 480 q^{68} + 960 q^{69} + 560 q^{70} + 856 q^{71} - 288 q^{72} - 1080 q^{73} - 1456 q^{74} + 2112 q^{75} + 640 q^{76} + 96 q^{78} + 1696 q^{79} - 640 q^{80} + 2592 q^{81} + 400 q^{82} + 2592 q^{83} + 3440 q^{85} - 2768 q^{86} + 912 q^{87} + 352 q^{88} - 3856 q^{89} - 720 q^{90} - 112 q^{91} + 1888 q^{92} + 1128 q^{93} + 1120 q^{94} + 4800 q^{95} + 2800 q^{97} - 392 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(462))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 11
462.4.a.a 462.a 1.a $1$ $27.259$ \(\Q\) None \(-2\) \(-3\) \(-21\) \(7\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-21q^{5}+6q^{6}+\cdots\)
462.4.a.b 462.a 1.a $1$ $27.259$ \(\Q\) None \(-2\) \(-3\) \(-14\) \(-7\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-14q^{5}+6q^{6}+\cdots\)
462.4.a.c 462.a 1.a $1$ $27.259$ \(\Q\) None \(-2\) \(-3\) \(11\) \(-7\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+11q^{5}+6q^{6}+\cdots\)
462.4.a.d 462.a 1.a $1$ $27.259$ \(\Q\) None \(-2\) \(3\) \(-7\) \(7\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots\)
462.4.a.e 462.a 1.a $1$ $27.259$ \(\Q\) None \(2\) \(-3\) \(-4\) \(-7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-4q^{5}-6q^{6}+\cdots\)
462.4.a.f 462.a 1.a $1$ $27.259$ \(\Q\) None \(2\) \(-3\) \(1\) \(-7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+q^{5}-6q^{6}+\cdots\)
462.4.a.g 462.a 1.a $1$ $27.259$ \(\Q\) None \(2\) \(-3\) \(3\) \(7\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+3q^{5}-6q^{6}+\cdots\)
462.4.a.h 462.a 1.a $1$ $27.259$ \(\Q\) None \(2\) \(3\) \(-17\) \(7\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-17q^{5}+6q^{6}+\cdots\)
462.4.a.i 462.a 1.a $1$ $27.259$ \(\Q\) None \(2\) \(3\) \(-13\) \(-7\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-13q^{5}+6q^{6}+\cdots\)
462.4.a.j 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{177}) \) None \(-4\) \(-6\) \(3\) \(14\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(1+\beta )q^{5}+6q^{6}+\cdots\)
462.4.a.k 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{697}) \) None \(-4\) \(-6\) \(7\) \(-14\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(4-\beta )q^{5}+6q^{6}+\cdots\)
462.4.a.l 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{113}) \) None \(-4\) \(-6\) \(14\) \(14\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(7-\beta )q^{5}+6q^{6}+\cdots\)
462.4.a.m 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{217}) \) None \(-4\) \(6\) \(7\) \(-14\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(4-\beta )q^{5}-6q^{6}+\cdots\)
462.4.a.n 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{89}) \) None \(4\) \(-6\) \(-17\) \(14\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-8-\beta )q^{5}+\cdots\)
462.4.a.o 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{817}) \) None \(4\) \(-6\) \(-3\) \(-14\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-1-\beta )q^{5}+\cdots\)
462.4.a.p 462.a 1.a $2$ $27.259$ \(\Q(\sqrt{793}) \) None \(4\) \(6\) \(-3\) \(-14\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-1-\beta )q^{5}+\cdots\)
462.4.a.q 462.a 1.a $3$ $27.259$ 3.3.768425.1 None \(-6\) \(9\) \(-7\) \(21\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
462.4.a.r 462.a 1.a $3$ $27.259$ 3.3.1028796.1 None \(-6\) \(9\) \(7\) \(-21\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(2+\beta _{1})q^{5}+\cdots\)
462.4.a.s 462.a 1.a $3$ $27.259$ 3.3.843032.1 None \(6\) \(9\) \(13\) \(21\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(4+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(462))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(462)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)