Properties

Label 495.2.a
Level $495$
Weight $2$
Character orbit 495.a
Rep. character $\chi_{495}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $7$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(495))\).

Total New Old
Modular forms 80 18 62
Cusp forms 65 18 47
Eisenstein series 15 0 15

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.
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(3\)
Minus space\(-\)\(15\)

Trace form

\( 18 q + 26 q^{4} + 2 q^{5} + 4 q^{7} + 12 q^{8} + O(q^{10}) \) \( 18 q + 26 q^{4} + 2 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 12 q^{13} + 20 q^{14} + 38 q^{16} - 4 q^{17} + 8 q^{19} + 2 q^{20} - 2 q^{22} + 4 q^{23} + 18 q^{25} - 16 q^{26} - 12 q^{28} + 4 q^{29} - 8 q^{31} + 24 q^{32} - 4 q^{35} + 20 q^{37} - 4 q^{41} + 12 q^{43} - 4 q^{44} - 28 q^{46} + 28 q^{47} + 42 q^{49} - 12 q^{52} + 12 q^{53} - 4 q^{55} + 12 q^{56} - 48 q^{58} - 4 q^{61} - 32 q^{62} - 6 q^{64} - 4 q^{65} + 4 q^{67} - 68 q^{68} - 20 q^{70} - 32 q^{71} + 12 q^{73} + 24 q^{74} - 40 q^{76} + 4 q^{77} + 32 q^{79} - 10 q^{80} - 64 q^{82} + 12 q^{83} + 12 q^{85} - 28 q^{86} - 6 q^{88} + 20 q^{89} - 32 q^{91} + 12 q^{92} - 68 q^{94} - 8 q^{95} + 36 q^{97} - 48 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(495))\) 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
495.2.a.a 495.a 1.a $1$ $3.953$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+q^{11}+\cdots\)
495.2.a.b 495.a 1.a $2$ $3.953$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
495.2.a.c 495.a 1.a $2$ $3.953$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
495.2.a.d 495.a 1.a $2$ $3.953$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
495.2.a.e 495.a 1.a $3$ $3.953$ 3.3.148.1 None \(1\) \(0\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
495.2.a.f 495.a 1.a $4$ $3.953$ 4.4.48704.2 None \(-2\) \(0\) \(-4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
495.2.a.g 495.a 1.a $4$ $3.953$ 4.4.48704.2 None \(2\) \(0\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(495))\) into lower level spaces

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