Properties

Label 462.8.a
Level $462$
Weight $8$
Character orbit 462.a
Rep. character $\chi_{462}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $17$
Sturm bound $768$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 462.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(768\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(462))\).

Total New Old
Modular forms 680 72 608
Cusp forms 664 72 592
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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(38\)
Minus space\(-\)\(34\)

Trace form

\( 72 q + 32 q^{2} + 4608 q^{4} - 440 q^{5} + 2048 q^{8} + 52488 q^{9} + O(q^{10}) \) \( 72 q + 32 q^{2} + 4608 q^{4} - 440 q^{5} + 2048 q^{8} + 52488 q^{9} - 12480 q^{10} + 7176 q^{13} + 294912 q^{16} - 30888 q^{17} + 23328 q^{18} - 90704 q^{19} - 28160 q^{20} + 42592 q^{22} - 19240 q^{23} + 1196136 q^{25} - 429824 q^{26} - 893384 q^{29} - 188488 q^{31} + 131072 q^{32} - 551744 q^{34} - 235984 q^{35} + 3359232 q^{36} + 442656 q^{37} + 502848 q^{38} - 798720 q^{40} + 699832 q^{41} + 296352 q^{42} + 1210680 q^{43} - 320760 q^{45} - 2140864 q^{46} + 2193560 q^{47} + 8470728 q^{49} - 186400 q^{50} - 1162728 q^{51} + 459264 q^{52} - 2995208 q^{53} + 1313024 q^{58} + 12326336 q^{59} + 7000744 q^{61} - 376064 q^{62} + 18874368 q^{64} - 4482784 q^{65} + 1949904 q^{67} - 1976832 q^{68} + 1578096 q^{69} + 2744000 q^{70} - 2920216 q^{71} + 1492992 q^{72} + 14713976 q^{73} + 4690624 q^{74} + 4728672 q^{75} - 5805056 q^{76} + 6348672 q^{78} - 20175360 q^{79} - 1802240 q^{80} + 38263752 q^{81} - 12275008 q^{82} + 18519072 q^{83} - 13824320 q^{85} + 8997824 q^{86} - 18507744 q^{87} + 2725888 q^{88} + 8416 q^{89} - 9097920 q^{90} + 13747440 q^{91} - 1231360 q^{92} - 21713400 q^{93} - 5076352 q^{94} + 2166960 q^{95} + 25772656 q^{97} + 3764768 q^{98} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(462))\) 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
462.8.a.a 462.a 1.a $1$ $144.322$ \(\Q\) None \(-8\) \(-27\) \(182\) \(343\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+182q^{5}+\cdots\)
462.8.a.b 462.a 1.a $3$ $144.322$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-24\) \(-81\) \(-30\) \(1029\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-10-5\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.c 462.a 1.a $3$ $144.322$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-24\) \(81\) \(-98\) \(1029\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-33-2\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.d 462.a 1.a $4$ $144.322$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(-108\) \(-12\) \(-1372\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-3-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.e 462.a 1.a $4$ $144.322$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(-108\) \(238\) \(-1372\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(59+\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.f 462.a 1.a $4$ $144.322$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(108\) \(238\) \(-1372\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(59+\beta _{2}+\cdots)q^{5}+\cdots\)
462.8.a.g 462.a 1.a $4$ $144.322$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(-108\) \(82\) \(1372\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(20-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.h 462.a 1.a $4$ $144.322$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(108\) \(-418\) \(1372\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-104+\beta _{2}+\cdots)q^{5}+\cdots\)
462.8.a.i 462.a 1.a $4$ $144.322$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(108\) \(-332\) \(-1372\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-83-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.j 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-40\) \(-135\) \(-98\) \(1715\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-20-\beta _{2}+\cdots)q^{5}+\cdots\)
462.8.a.k 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-40\) \(135\) \(-98\) \(1715\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-20+\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.l 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-40\) \(135\) \(238\) \(-1715\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(48-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.m 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(-135\) \(-418\) \(1715\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-84-\beta _{2}+\cdots)q^{5}+\cdots\)
462.8.a.n 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(-135\) \(-82\) \(-1715\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-2^{4}-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.o 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(-135\) \(-82\) \(-1715\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-2^{4}-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.p 462.a 1.a $5$ $144.322$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(135\) \(-82\) \(-1715\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-2^{4}-\beta _{1}+\cdots)q^{5}+\cdots\)
462.8.a.q 462.a 1.a $6$ $144.322$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(48\) \(162\) \(332\) \(2058\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(55+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(462))\) into lower level spaces

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