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Properties

Label 1260.2.s
Level $1260$
Weight $2$
Character orbit 1260.s
Rep. character $\chi_{1260}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $8$
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.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
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 624 28 596
Cusp forms 528 28 500
Eisenstein series 96 0 96

Trace form

\( 28 q - 2 q^{5} + 2 q^{7} + O(q^{10}) \) \( 28 q - 2 q^{5} + 2 q^{7} - 16 q^{13} - 12 q^{17} - 4 q^{19} - 6 q^{23} - 14 q^{25} - 4 q^{29} + 20 q^{37} + 20 q^{41} + 4 q^{43} + 16 q^{47} + 10 q^{49} + 16 q^{53} + 8 q^{55} - 12 q^{59} + 2 q^{61} + 14 q^{67} - 64 q^{71} + 32 q^{77} + 12 q^{79} + 52 q^{83} + 8 q^{85} - 6 q^{89} - 48 q^{91} + 8 q^{95} - 24 q^{97} + O(q^{100}) \)

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.s.a 1260.s 7.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
1260.2.s.b 1260.s 7.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1260.2.s.c 1260.s 7.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1260.2.s.d 1260.s 7.c $2$ $10.061$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
1260.2.s.e 1260.s 7.c $4$ $10.061$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots\)
1260.2.s.f 1260.s 7.c $4$ $10.061$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
1260.2.s.g 1260.s 7.c $6$ $10.061$ 6.0.4406832.1 None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{5}-\beta _{4}q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
1260.2.s.h 1260.s 7.c $6$ $10.061$ 6.0.4406832.1 None \(0\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{5}-\beta _{4}q^{7}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)