Properties

Label 273.2.by
Level $273$
Weight $2$
Character orbit 273.by
Rep. character $\chi_{273}(76,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
Newform subspaces $4$
Sturm bound $74$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

Total New Old
Modular forms 168 72 96
Cusp forms 136 72 64
Eisenstein series 32 0 32

Trace form

\( 72 q - 2 q^{7} + 36 q^{9} + O(q^{10}) \) \( 72 q - 2 q^{7} + 36 q^{9} - 16 q^{11} + 48 q^{14} + 24 q^{16} - 10 q^{21} - 16 q^{22} - 56 q^{28} - 8 q^{29} - 40 q^{32} - 8 q^{35} - 28 q^{37} + 8 q^{39} - 12 q^{42} - 12 q^{43} - 16 q^{44} - 112 q^{46} - 30 q^{49} + 176 q^{50} - 112 q^{53} - 180 q^{56} + 48 q^{57} + 48 q^{58} - 104 q^{60} - 4 q^{63} + 32 q^{65} + 16 q^{67} - 56 q^{70} - 24 q^{71} - 16 q^{74} - 8 q^{78} + 48 q^{79} - 36 q^{81} + 20 q^{84} - 56 q^{85} - 48 q^{86} + 216 q^{88} + 86 q^{91} - 80 q^{92} + 12 q^{93} + 96 q^{95} + 36 q^{98} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.by.a 273.by 91.ac $4$ $2.180$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
273.2.by.b 273.by 91.ac $4$ $2.180$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
273.2.by.c 273.by 91.ac $32$ $2.180$ None \(-2\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
273.2.by.d 273.by 91.ac $32$ $2.180$ None \(-2\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)