Properties

Label 495.2.n
Level $495$
Weight $2$
Character orbit 495.n
Rep. character $\chi_{495}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $80$
Newform subspaces $8$
Sturm bound $144$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 8 \)
Sturm bound: \(144\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 320 80 240
Cusp forms 256 80 176
Eisenstein series 64 0 64

Trace form

\( 80 q - 2 q^{2} - 24 q^{4} - 4 q^{7} + 14 q^{8} + O(q^{10}) \) \( 80 q - 2 q^{2} - 24 q^{4} - 4 q^{7} + 14 q^{8} + 8 q^{10} + 6 q^{11} + 2 q^{13} - 16 q^{16} + 28 q^{17} + 14 q^{19} - 4 q^{20} - 62 q^{22} + 16 q^{23} - 20 q^{25} - 20 q^{26} + 22 q^{28} - 18 q^{29} - 12 q^{31} - 84 q^{32} - 16 q^{34} + 4 q^{35} + 20 q^{37} + 42 q^{38} - 6 q^{40} + 24 q^{41} + 20 q^{43} - 12 q^{44} + 18 q^{46} + 28 q^{47} + 2 q^{49} - 2 q^{50} + 58 q^{52} - 32 q^{53} - 12 q^{55} - 52 q^{56} - 26 q^{58} - 18 q^{59} - 52 q^{61} + 52 q^{62} - 28 q^{64} - 40 q^{65} - 8 q^{67} - 6 q^{68} - 40 q^{70} - 44 q^{71} - 42 q^{73} + 16 q^{74} - 112 q^{76} + 86 q^{77} - 2 q^{79} - 32 q^{80} + 54 q^{82} + 2 q^{83} - 16 q^{85} + 90 q^{86} + 98 q^{88} + 48 q^{89} - 48 q^{91} - 12 q^{92} - 6 q^{94} + 16 q^{95} + 60 q^{97} - 28 q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.2.n.a $8$ $3.953$ 8.0.13140625.1 None \(-4\) \(0\) \(2\) \(3\) \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
495.2.n.b $8$ $3.953$ 8.0.819390625.1 None \(-2\) \(0\) \(-2\) \(9\) \(q-\beta _{4}q^{2}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
495.2.n.c $8$ $3.953$ \(\Q(\zeta_{15})\) None \(-2\) \(0\) \(2\) \(-5\) \(q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
495.2.n.d $8$ $3.953$ 8.0.13140625.1 None \(0\) \(0\) \(-2\) \(1\) \(q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{4}+\cdots\)
495.2.n.e $8$ $3.953$ 8.0.13140625.1 None \(2\) \(0\) \(-2\) \(-1\) \(q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{6}-\beta _{7})q^{4}+\cdots\)
495.2.n.f $8$ $3.953$ 8.0.159390625.1 None \(4\) \(0\) \(2\) \(-3\) \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
495.2.n.g $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(0\) \(-4\) \(-4\) \(q+(1-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{10}-\beta _{14}+\cdots)q^{2}+\cdots\)
495.2.n.h $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(2\) \(0\) \(4\) \(-4\) \(q+(-1+\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10}+\beta _{14}+\cdots)q^{2}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)