Properties

Label 1260.2.t
Level $1260$
Weight $2$
Character orbit 1260.t
Rep. character $\chi_{1260}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $5$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 600 64 536
Cusp forms 552 64 488
Eisenstein series 48 0 48

Trace form

\( 64 q - 8 q^{5} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 64 q - 8 q^{5} - 2 q^{7} - 4 q^{9} - 4 q^{11} + 2 q^{13} - 2 q^{15} + 16 q^{17} - 4 q^{19} + 12 q^{23} + 64 q^{25} + 6 q^{27} - 2 q^{29} - 4 q^{31} - 20 q^{33} + 2 q^{37} + 32 q^{39} + 14 q^{41} - 4 q^{43} - 2 q^{45} + 12 q^{47} + 10 q^{49} + 6 q^{51} + 16 q^{53} + 26 q^{57} - 10 q^{59} + 20 q^{61} + 42 q^{63} + 2 q^{65} + 14 q^{67} + 64 q^{69} + 8 q^{71} - 28 q^{73} - 22 q^{77} + 8 q^{79} - 52 q^{81} + 24 q^{83} + 6 q^{85} + 54 q^{87} + 2 q^{89} - 10 q^{91} - 36 q^{93} + 2 q^{97} + 58 q^{99} + O(q^{100}) \)

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.t.a 1260.t 63.g $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}-q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1260.2.t.b 1260.t 63.g $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}-q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1260.2.t.c 1260.t 63.g $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1260.2.t.d 1260.t 63.g $26$ $10.061$ None \(0\) \(-1\) \(26\) \(3\) $\mathrm{SU}(2)[C_{3}]$
1260.2.t.e 1260.t 63.g $32$ $10.061$ None \(0\) \(1\) \(-32\) \(-4\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)