Properties

Label 1260.2.bm
Level $1260$
Weight $2$
Character orbit 1260.bm
Rep. character $\chi_{1260}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $4$
Sturm bound $576$
Trace bound $5$

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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 624 40 584
Cusp forms 528 40 488
Eisenstein series 96 0 96

Trace form

\( 40 q - q^{5} + O(q^{10}) \) \( 40 q - q^{5} + 2 q^{11} - 10 q^{19} + 3 q^{25} - 20 q^{29} - 6 q^{31} - 15 q^{35} + 12 q^{41} + 2 q^{49} + 14 q^{55} + 26 q^{59} + 16 q^{61} + 10 q^{65} + 32 q^{71} + 14 q^{79} - 58 q^{85} + 44 q^{89} - 4 q^{91} + 7 q^{95} + O(q^{100}) \)

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.bm.a 1260.bm 35.j $4$ $10.061$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
1260.2.bm.b 1260.bm 35.j $4$ $10.061$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(2\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{5}+(2-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
1260.2.bm.c 1260.bm 35.j $16$ $10.061$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{8}-\beta _{12}-\beta _{14})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1260.2.bm.d 1260.bm 35.j $16$ $10.061$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{5}+(\beta _{5}-\beta _{6}+\beta _{14})q^{7}-\beta _{15}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)