↑

Properties

Label 1260.2.r
Level $1260$
Weight $2$
Character orbit 1260.r
Rep. character $\chi_{1260}(421,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $9$
Sturm bound $576$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

Total New Old
Modular forms 600 48 552
Cusp forms 552 48 504
Eisenstein series 48 0 48

Trace form

\( 48 q - 4 q^{3} - 8 q^{9} + O(q^{10}) \) \( 48 q - 4 q^{3} - 8 q^{9} + 2 q^{11} + 2 q^{15} - 8 q^{17} - 24 q^{19} + 2 q^{21} - 24 q^{25} - 16 q^{27} - 8 q^{29} + 16 q^{33} + 8 q^{35} + 30 q^{39} - 4 q^{41} + 12 q^{43} + 8 q^{45} + 24 q^{47} - 24 q^{49} - 6 q^{51} + 64 q^{53} + 48 q^{57} + 20 q^{59} + 8 q^{63} - 18 q^{65} + 12 q^{67} - 44 q^{69} - 40 q^{71} - 24 q^{73} - 4 q^{75} - 16 q^{77} - 6 q^{79} - 8 q^{81} - 36 q^{83} - 6 q^{85} + 36 q^{87} + 8 q^{89} + 12 q^{91} - 56 q^{93} - 8 q^{95} + 12 q^{97} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1260.2.r.a 1260.r 9.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1260.2.r.b 1260.r 9.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1260.2.r.c 1260.r 9.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1260.2.r.d 1260.r 9.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1260.2.r.e 1260.r 9.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
1260.2.r.f 1260.r 9.c $8$ $10.061$ 8.0.3830743449.1 None \(0\) \(-3\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(-1-\beta _{5})q^{5}+\beta _{5}q^{7}+(-2+\cdots)q^{9}+\cdots\)
1260.2.r.g 1260.r 9.c $8$ $10.061$ 8.0.152695449.1 None \(0\) \(-1\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}-2\beta _{6}+\cdots)q^{3}+\cdots\)
1260.2.r.h 1260.r 9.c $8$ $10.061$ 8.0.1223810289.2 None \(0\) \(-1\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}-\beta _{7})q^{3}+\beta _{4}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
1260.2.r.i 1260.r 9.c $14$ $10.061$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(1\) \(7\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(1+\beta _{8})q^{5}-\beta _{8}q^{7}+\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)