Properties

Label 495.2.c
Level $495$
Weight $2$
Character orbit 495.c
Rep. character $\chi_{495}(199,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $5$
Sturm bound $144$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24 q - 18 q^{4} - q^{5} + O(q^{10}) \) \( 24 q - 18 q^{4} - q^{5} - 6 q^{10} + 4 q^{11} + 4 q^{14} + 10 q^{16} + 16 q^{19} + 8 q^{20} + 5 q^{25} + 24 q^{26} + 12 q^{29} - 30 q^{31} - 40 q^{34} - 18 q^{35} + 8 q^{40} - 12 q^{41} - 14 q^{44} + 56 q^{46} - 24 q^{49} + 10 q^{50} + 3 q^{55} - 36 q^{56} - 18 q^{59} - 4 q^{61} - 14 q^{64} - 40 q^{65} + 32 q^{70} + 54 q^{71} - 44 q^{74} - 40 q^{76} + 20 q^{79} + 46 q^{80} + 10 q^{85} + 28 q^{86} + 34 q^{89} - 12 q^{94} + 36 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.2.c.a 495.c 5.b $4$ $3.953$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
495.2.c.b 495.c 5.b $4$ $3.953$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
495.2.c.c 495.c 5.b $4$ $3.953$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
495.2.c.d 495.c 5.b $6$ $3.953$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
495.2.c.e 495.c 5.b $6$ $3.953$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)