Properties

Label 462.6.a
Level $462$
Weight $6$
Character orbit 462.a
Rep. character $\chi_{462}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $20$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 462.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(462))\).

Total New Old
Modular forms 488 48 440
Cusp forms 472 48 424
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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(22\)
Minus space\(-\)\(26\)

Trace form

\( 48 q + 16 q^{2} + 768 q^{4} - 88 q^{5} + 256 q^{8} + 3888 q^{9} + O(q^{10}) \) \( 48 q + 16 q^{2} + 768 q^{4} - 88 q^{5} + 256 q^{8} + 3888 q^{9} - 1248 q^{10} + 552 q^{13} + 12288 q^{16} - 8712 q^{17} + 1296 q^{18} + 1136 q^{19} - 1408 q^{20} - 1936 q^{22} - 392 q^{23} + 27936 q^{25} - 16576 q^{26} + 25016 q^{29} + 8728 q^{31} + 4096 q^{32} + 20576 q^{34} + 24304 q^{35} + 62208 q^{36} - 22224 q^{37} - 2016 q^{38} - 19968 q^{40} + 19928 q^{41} - 7056 q^{42} + 9528 q^{43} - 7128 q^{45} + 23584 q^{46} + 29560 q^{47} + 115248 q^{49} - 3728 q^{50} + 12888 q^{51} + 8832 q^{52} + 79928 q^{53} - 14144 q^{58} - 184448 q^{59} + 59912 q^{61} + 58112 q^{62} + 196608 q^{64} - 90752 q^{65} - 36432 q^{67} - 139392 q^{68} - 47664 q^{69} - 39200 q^{70} + 82120 q^{71} + 20736 q^{72} - 244712 q^{73} + 58592 q^{74} - 117792 q^{75} + 18176 q^{76} + 6336 q^{78} + 96384 q^{79} - 22528 q^{80} + 314928 q^{81} - 199712 q^{82} - 5280 q^{83} - 228256 q^{85} + 101344 q^{86} + 120672 q^{87} - 30976 q^{88} - 128368 q^{89} - 101088 q^{90} - 11760 q^{91} - 6272 q^{92} + 167256 q^{93} + 134848 q^{94} - 384528 q^{95} - 206080 q^{97} + 38416 q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(462))\) 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
462.6.a.a 462.a 1.a $1$ $74.097$ \(\Q\) None \(-4\) \(-9\) \(-78\) \(49\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-78q^{5}+6^{2}q^{6}+\cdots\)
462.6.a.b 462.a 1.a $1$ $74.097$ \(\Q\) None \(-4\) \(-9\) \(44\) \(-49\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+44q^{5}+6^{2}q^{6}+\cdots\)
462.6.a.c 462.a 1.a $1$ $74.097$ \(\Q\) None \(-4\) \(-9\) \(106\) \(-49\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+106q^{5}+6^{2}q^{6}+\cdots\)
462.6.a.d 462.a 1.a $1$ $74.097$ \(\Q\) None \(4\) \(-9\) \(-6\) \(-49\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-6q^{5}-6^{2}q^{6}+\cdots\)
462.6.a.e 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{498}) \) None \(-8\) \(-18\) \(-98\) \(-98\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-7^{2}q^{5}+6^{2}q^{6}+\cdots\)
462.6.a.f 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{214}) \) None \(-8\) \(-18\) \(-86\) \(-98\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-43+2\beta )q^{5}+\cdots\)
462.6.a.g 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{191}) \) None \(-8\) \(-18\) \(70\) \(98\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(35+2\beta )q^{5}+\cdots\)
462.6.a.h 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{14239}) \) None \(-8\) \(-18\) \(98\) \(98\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+7^{2}q^{5}+6^{2}q^{6}+\cdots\)
462.6.a.i 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{7}) \) None \(-8\) \(18\) \(-42\) \(-98\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-21+10\beta )q^{5}+\cdots\)
462.6.a.j 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{14}) \) None \(-8\) \(18\) \(70\) \(98\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(35+4\beta )q^{5}+\cdots\)
462.6.a.k 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{103}) \) None \(8\) \(-18\) \(-50\) \(-98\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-5^{2}+4\beta )q^{5}+\cdots\)
462.6.a.l 462.a 1.a $2$ $74.097$ \(\Q(\sqrt{71}) \) None \(8\) \(18\) \(-94\) \(98\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-47+2\beta )q^{5}+\cdots\)
462.6.a.m 462.a 1.a $3$ $74.097$ 3.3.1438780.1 None \(-12\) \(27\) \(-42\) \(-147\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-15-2\beta _{1}+\cdots)q^{5}+\cdots\)
462.6.a.n 462.a 1.a $3$ $74.097$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(-27\) \(-56\) \(-147\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-19+\beta _{2})q^{5}+\cdots\)
462.6.a.o 462.a 1.a $3$ $74.097$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(-27\) \(56\) \(147\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(19+\beta _{1})q^{5}+\cdots\)
462.6.a.p 462.a 1.a $3$ $74.097$ 3.3.172392.1 None \(12\) \(27\) \(-56\) \(-147\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-18-3\beta _{1}+\cdots)q^{5}+\cdots\)
462.6.a.q 462.a 1.a $4$ $74.097$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(36\) \(70\) \(196\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(17+\beta _{1})q^{5}+\cdots\)
462.6.a.r 462.a 1.a $4$ $74.097$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(-36\) \(-44\) \(196\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-11+\beta _{1}+\cdots)q^{5}+\cdots\)
462.6.a.s 462.a 1.a $4$ $74.097$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(36\) \(-6\) \(-196\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
462.6.a.t 462.a 1.a $4$ $74.097$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(36\) \(56\) \(196\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(14-\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(462))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(462)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)