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.

\(3\)\(5\)\(11\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(42\)\(6\)\(36\)\(40\)\(6\)\(34\)\(2\)\(0\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(50\)\(10\)\(40\)\(48\)\(10\)\(38\)\(2\)\(0\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(46\)\(10\)\(36\)\(44\)\(10\)\(34\)\(2\)\(0\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(46\)\(6\)\(40\)\(44\)\(6\)\(38\)\(2\)\(0\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(48\)\(13\)\(35\)\(46\)\(13\)\(33\)\(2\)\(0\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(44\)\(11\)\(33\)\(42\)\(11\)\(31\)\(2\)\(0\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(44\)\(12\)\(32\)\(42\)\(12\)\(30\)\(2\)\(0\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(48\)\(14\)\(34\)\(46\)\(14\)\(32\)\(2\)\(0\)\(2\)
Plus space\(+\)\(176\)\(35\)\(141\)\(168\)\(35\)\(133\)\(8\)\(0\)\(8\)
Minus space\(-\)\(192\)\(47\)\(145\)\(184\)\(47\)\(137\)\(8\)\(0\)\(8\)

Trace form

\( 82 q + 1268 q^{4} + 50 q^{5} - 44 q^{7} - 852 q^{8} - 100 q^{10} + 1748 q^{13} - 2720 q^{14} + 20160 q^{16} - 956 q^{17} + 2728 q^{19} + 4300 q^{20} - 968 q^{22} + 7556 q^{23} + 51250 q^{25} + 3292 q^{26}+ \cdots + 481168 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist 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 165.6.a.e \(-7\) \(0\) \(75\) \(92\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(24+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.b 495.a 1.a $3$ $79.390$ 3.3.18257.1 None 165.6.a.c \(-2\) \(0\) \(-75\) \(-68\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-14-\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.c 495.a 1.a $3$ $79.390$ 3.3.788.1 None 165.6.a.d \(-2\) \(0\) \(-75\) \(152\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-8-4\beta _{1})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.d 495.a 1.a $3$ $79.390$ 3.3.3368.1 None 165.6.a.b \(2\) \(0\) \(75\) \(-232\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(8+4\beta _{2})q^{4}+5^{2}q^{5}+\cdots\)
495.6.a.e 495.a 1.a $3$ $79.390$ 3.3.34253.1 None 165.6.a.a \(7\) \(0\) \(-75\) \(-172\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(7+4\beta _{1}+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.f 495.a 1.a $3$ $79.390$ 3.3.21865.1 None 55.6.a.a \(7\) \(0\) \(-75\) \(-102\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{2})q^{2}+(12+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.g 495.a 1.a $4$ $79.390$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 55.6.a.b \(5\) \(0\) \(100\) \(-90\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(15+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
495.6.a.h 495.a 1.a $5$ $79.390$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 55.6.a.c \(-9\) \(0\) \(-125\) \(70\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(24-3\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.i 495.a 1.a $5$ $79.390$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 165.6.a.g \(1\) \(0\) \(125\) \(116\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5^{2}+\beta _{1}+\beta _{3})q^{4}+5^{2}q^{5}+\cdots\)
495.6.a.j 495.a 1.a $5$ $79.390$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 165.6.a.f \(2\) \(0\) \(125\) \(184\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2^{4}+\beta _{2})q^{4}+5^{2}q^{5}+(37+\cdots)q^{7}+\cdots\)
495.6.a.k 495.a 1.a $6$ $79.390$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 495.6.a.k \(-5\) \(0\) \(150\) \(-80\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(9-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.6.a.l 495.a 1.a $6$ $79.390$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 55.6.a.d \(-3\) \(0\) \(150\) \(-66\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(20-\beta _{1}+\beta _{3}+\beta _{5})q^{4}+\cdots\)
495.6.a.m 495.a 1.a $6$ $79.390$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 495.6.a.k \(5\) \(0\) \(-150\) \(-80\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(9-2\beta _{1}+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
495.6.a.n 495.a 1.a $7$ $79.390$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 165.6.a.h \(-1\) \(0\) \(-175\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(28+\beta _{2})q^{4}-5^{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
495.6.a.o 495.a 1.a $10$ $79.390$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 495.6.a.o \(-3\) \(0\) \(-250\) \(116\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(18+\beta _{2})q^{4}-5^{2}q^{5}+(12+\cdots)q^{7}+\cdots\)
495.6.a.p 495.a 1.a $10$ $79.390$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 495.6.a.o \(3\) \(0\) \(250\) \(116\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(18+\beta _{2})q^{4}+5^{2}q^{5}+(12+\cdots)q^{7}+\cdots\)

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

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