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Properties

Label 495.4.a
Level $495$
Weight $4$
Character orbit 495.a
Rep. character $\chi_{495}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $16$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 495.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(495))\).

Total New Old
Modular forms 224 50 174
Cusp forms 208 50 158
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
\(+\)\(+\)\(+\)$+$\(7\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(7\)
\(-\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(8\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(31\)
Minus space\(-\)\(19\)

Trace form

\( 50 q + 188 q^{4} - 10 q^{5} + 88 q^{7} + 12 q^{8} + O(q^{10}) \) \( 50 q + 188 q^{4} - 10 q^{5} + 88 q^{7} + 12 q^{8} + 60 q^{10} - 104 q^{13} + 40 q^{14} + 864 q^{16} + 64 q^{17} + 152 q^{19} - 140 q^{20} + 44 q^{22} - 208 q^{23} + 1250 q^{25} + 1108 q^{26} + 1500 q^{28} + 116 q^{29} + 636 q^{31} + 1216 q^{32} + 184 q^{34} + 40 q^{35} + 84 q^{37} - 1088 q^{38} + 600 q^{40} + 484 q^{41} - 712 q^{43} - 308 q^{44} - 128 q^{46} - 1440 q^{47} + 1454 q^{49} + 1036 q^{52} - 1300 q^{53} + 220 q^{55} + 960 q^{56} + 2880 q^{58} + 2584 q^{59} + 2004 q^{61} + 3896 q^{62} + 5116 q^{64} + 160 q^{65} + 2856 q^{67} + 3708 q^{68} - 700 q^{70} + 628 q^{71} - 128 q^{73} + 352 q^{74} + 2224 q^{76} - 792 q^{77} + 256 q^{79} - 400 q^{80} - 3728 q^{82} + 2344 q^{83} - 320 q^{85} - 4084 q^{86} + 528 q^{88} + 312 q^{89} + 952 q^{91} + 3200 q^{92} - 2280 q^{94} + 1560 q^{95} + 3268 q^{97} - 7184 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(495))\) 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
495.4.a.a 495.a 1.a $1$ $29.206$ \(\Q\) None \(-1\) \(0\) \(5\) \(-9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+5q^{5}-9q^{7}+15q^{8}+\cdots\)
495.4.a.b 495.a 1.a $1$ $29.206$ \(\Q\) None \(-1\) \(0\) \(5\) \(36\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+5q^{5}+6^{2}q^{7}+15q^{8}+\cdots\)
495.4.a.c 495.a 1.a $1$ $29.206$ \(\Q\) None \(0\) \(0\) \(5\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{4}+5q^{5}+2q^{7}+11q^{11}-22q^{13}+\cdots\)
495.4.a.d 495.a 1.a $2$ $29.206$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(10\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-4+\beta )q^{4}+5q^{5}+(-4+\cdots)q^{7}+\cdots\)
495.4.a.e 495.a 1.a $2$ $29.206$ \(\Q(\sqrt{17}) \) None \(7\) \(0\) \(-10\) \(-25\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(4-\beta )q^{2}+(12-7\beta )q^{4}-5q^{5}+(-8+\cdots)q^{7}+\cdots\)
495.4.a.f 495.a 1.a $3$ $29.206$ 3.3.568.1 None \(-5\) \(0\) \(15\) \(-15\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}+\beta _{2})q^{2}+(7+2\beta _{1})q^{4}+\cdots\)
495.4.a.g 495.a 1.a $3$ $29.206$ 3.3.788.1 None \(-1\) \(0\) \(-15\) \(-16\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-2-\beta _{1})q^{4}-5q^{5}+(-3+\cdots)q^{7}+\cdots\)
495.4.a.h 495.a 1.a $3$ $29.206$ 3.3.1772.1 None \(-1\) \(0\) \(-15\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+2\beta _{2})q^{4}-5q^{5}+(2+\cdots)q^{7}+\cdots\)
495.4.a.i 495.a 1.a $3$ $29.206$ 3.3.1957.1 None \(-1\) \(0\) \(-15\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(6+\beta _{1}+2\beta _{2})q^{4}-5q^{5}+\cdots\)
495.4.a.j 495.a 1.a $3$ $29.206$ 3.3.1772.1 None \(1\) \(0\) \(15\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{2})q^{4}+5q^{5}+(2+\cdots)q^{7}+\cdots\)
495.4.a.k 495.a 1.a $3$ $29.206$ 3.3.47528.1 None \(2\) \(0\) \(15\) \(10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(10+\beta _{2})q^{4}+5q^{5}+\cdots\)
495.4.a.l 495.a 1.a $3$ $29.206$ 3.3.23612.1 None \(4\) \(0\) \(15\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(7+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
495.4.a.m 495.a 1.a $4$ $29.206$ 4.4.1540841.1 None \(-4\) \(0\) \(-20\) \(34\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
495.4.a.n 495.a 1.a $4$ $29.206$ 4.4.1539480.1 None \(-1\) \(0\) \(-20\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(5+\beta _{1}+\beta _{3})q^{4}-5q^{5}+\cdots\)
495.4.a.o 495.a 1.a $7$ $29.206$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-5\) \(0\) \(-35\) \(30\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+\cdots\)
495.4.a.p 495.a 1.a $7$ $29.206$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(5\) \(0\) \(35\) \(30\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(495))\) into lower level spaces

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