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Properties

Label 495.2.bc
Level $495$
Weight $2$
Character orbit 495.bc
Rep. character $\chi_{495}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
Newform subspaces $4$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 304 240 64
Cusp forms 272 240 32
Eisenstein series 32 0 32

Trace form

\( 240 q + 2 q^{3} - 16 q^{6} + O(q^{10}) \) \( 240 q + 2 q^{3} - 16 q^{6} - 8 q^{12} - 4 q^{15} + 120 q^{16} - 72 q^{18} - 24 q^{20} + 16 q^{21} - 48 q^{23} - 6 q^{25} - 28 q^{27} - 88 q^{30} - 120 q^{32} + 4 q^{33} + 48 q^{36} - 12 q^{37} + 24 q^{41} - 56 q^{42} + 52 q^{45} - 96 q^{46} + 36 q^{47} + 64 q^{48} + 32 q^{51} - 12 q^{55} + 72 q^{56} - 4 q^{57} - 40 q^{60} - 24 q^{61} - 88 q^{63} - 144 q^{65} - 6 q^{67} - 144 q^{68} - 192 q^{72} - 52 q^{75} - 24 q^{76} + 148 q^{78} + 52 q^{81} - 96 q^{82} - 48 q^{85} + 216 q^{86} + 104 q^{87} + 16 q^{90} - 144 q^{92} + 26 q^{93} + 120 q^{95} + 88 q^{96} - 54 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bc.a 495.bc 45.l $4$ $3.953$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
495.2.bc.b 495.bc 45.l $4$ $3.953$ \(\Q(\zeta_{12})\) None \(4\) \(-6\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
495.2.bc.c 495.bc 45.l $116$ $3.953$ None \(-4\) \(8\) \(2\) \(8\) $\mathrm{SU}(2)[C_{12}]$
495.2.bc.d 495.bc 45.l $116$ $3.953$ None \(-2\) \(0\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{12}]$

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

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