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Properties

Label 945.2.cj
Level $945$
Weight $2$
Character orbit 945.cj
Rep. character $\chi_{945}(208,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
Newform subspaces $5$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.cj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 624 208 416
Cusp forms 528 176 352
Eisenstein series 96 32 64

Trace form

\( 176 q - 2 q^{2} - 2 q^{7} + 8 q^{8} + O(q^{10}) \) \( 176 q - 2 q^{2} - 2 q^{7} + 8 q^{8} - 12 q^{10} + 68 q^{16} + 30 q^{17} + 48 q^{20} - 12 q^{22} - 12 q^{23} - 4 q^{25} + 24 q^{26} + 4 q^{28} - 12 q^{31} - 30 q^{32} + 44 q^{35} - 4 q^{37} + 12 q^{41} - 4 q^{43} - 20 q^{46} + 6 q^{47} + 28 q^{50} - 16 q^{53} + 88 q^{56} - 44 q^{58} - 48 q^{61} - 26 q^{65} + 2 q^{67} - 42 q^{70} + 64 q^{71} - 12 q^{73} - 48 q^{76} + 106 q^{77} - 12 q^{80} - 24 q^{82} - 84 q^{83} - 4 q^{85} - 80 q^{86} - 84 q^{88} - 16 q^{91} + 8 q^{92} + 50 q^{95} - 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.cj.a 945.cj 315.bg $4$ $7.546$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-8\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}+\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
945.2.cj.b 945.cj 315.bg $4$ $7.546$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}+\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
945.2.cj.c 945.cj 315.bg $4$ $7.546$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
945.2.cj.d 945.cj 315.bg $4$ $7.546$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
945.2.cj.e 945.cj 315.bg $160$ $7.546$ None \(2\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)