Properties

Label 495.6.a
Level $495$
Weight $6$
Character orbit 495.a
Rep. character $\chi_{495}(1,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $16$
Sturm bound $432$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 495.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(432\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(495))\).

Total New Old
Modular forms 368 82 286
Cusp forms 352 82 270
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.

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(14\)
Plus space\(+\)\(35\)
Minus space\(-\)\(47\)

Trace form

\( 82 q + 1268 q^{4} + 50 q^{5} - 44 q^{7} - 852 q^{8} + O(q^{10}) \) \( 82 q + 1268 q^{4} + 50 q^{5} - 44 q^{7} - 852 q^{8} - 100 q^{10} + 1748 q^{13} - 2720 q^{14} + 20160 q^{16} - 956 q^{17} + 2728 q^{19} + 4300 q^{20} - 968 q^{22} + 7556 q^{23} + 51250 q^{25} + 3292 q^{26} - 1028 q^{28} - 10876 q^{29} + 3480 q^{31} - 16064 q^{32} + 13672 q^{34} + 3100 q^{35} + 6020 q^{37} + 61120 q^{38} + 3000 q^{40} + 25852 q^{41} + 47628 q^{43} - 2420 q^{44} + 93512 q^{46} + 9372 q^{47} + 194210 q^{49} + 8972 q^{52} + 95708 q^{53} - 12100 q^{55} - 211872 q^{56} - 140352 q^{58} - 91808 q^{59} + 137852 q^{61} + 60392 q^{62} + 374844 q^{64} + 100 q^{65} - 9564 q^{67} + 231228 q^{68} + 20500 q^{70} - 79232 q^{71} - 93772 q^{73} + 68752 q^{74} + 384528 q^{76} + 76956 q^{77} + 92256 q^{79} + 134000 q^{80} + 392144 q^{82} - 178292 q^{83} - 134300 q^{85} + 522620 q^{86} - 46464 q^{88} - 373284 q^{89} + 90656 q^{91} - 220912 q^{92} + 668768 q^{94} + 19800 q^{95} - 420796 q^{97} + 481168 q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(495))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11
495.6.a.a 495.a 1.a $3$ $79.390$ 3.3.307532.1 None \(-7\) \(0\) \(75\) \(92\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(24+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.b 495.a 1.a $3$ $79.390$ 3.3.18257.1 None \(-2\) \(0\) \(-75\) \(-68\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-14-\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.c 495.a 1.a $3$ $79.390$ 3.3.788.1 None \(-2\) \(0\) \(-75\) \(152\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-8-4\beta _{1})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.d 495.a 1.a $3$ $79.390$ 3.3.3368.1 None \(2\) \(0\) \(75\) \(-232\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(8+4\beta _{2})q^{4}+5^{2}q^{5}+\cdots\)
495.6.a.e 495.a 1.a $3$ $79.390$ 3.3.34253.1 None \(7\) \(0\) \(-75\) \(-172\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(7+4\beta _{1}+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.f 495.a 1.a $3$ $79.390$ 3.3.21865.1 None \(7\) \(0\) \(-75\) \(-102\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{2})q^{2}+(12+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.g 495.a 1.a $4$ $79.390$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(5\) \(0\) \(100\) \(-90\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(15+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
495.6.a.h 495.a 1.a $5$ $79.390$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-9\) \(0\) \(-125\) \(70\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(24-3\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.i 495.a 1.a $5$ $79.390$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(0\) \(125\) \(116\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5^{2}+\beta _{1}+\beta _{3})q^{4}+5^{2}q^{5}+\cdots\)
495.6.a.j 495.a 1.a $5$ $79.390$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(2\) \(0\) \(125\) \(184\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2^{4}+\beta _{2})q^{4}+5^{2}q^{5}+(37+\cdots)q^{7}+\cdots\)
495.6.a.k 495.a 1.a $6$ $79.390$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-5\) \(0\) \(150\) \(-80\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(9-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.l 495.a 1.a $6$ $79.390$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-3\) \(0\) \(150\) \(-66\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(20-\beta _{1}+\beta _{3}+\beta _{5})q^{4}+\cdots\)
495.6.a.m 495.a 1.a $6$ $79.390$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(5\) \(0\) \(-150\) \(-80\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(9-2\beta _{1}+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.n 495.a 1.a $7$ $79.390$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(0\) \(-175\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(28+\beta _{2})q^{4}-5^{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
495.6.a.o 495.a 1.a $10$ $79.390$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(0\) \(-250\) \(116\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(18+\beta _{2})q^{4}-5^{2}q^{5}+(12+\cdots)q^{7}+\cdots\)
495.6.a.p 495.a 1.a $10$ $79.390$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(0\) \(250\) \(116\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(18+\beta _{2})q^{4}+5^{2}q^{5}+(12+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(495))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(495)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)