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Properties

Label 207.2.i
Level $207$
Weight $2$
Character orbit 207.i
Rep. character $\chi_{207}(55,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $90$
Newform subspaces $5$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 207.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(207, [\chi])\).

Total New Old
Modular forms 280 110 170
Cusp forms 200 90 110
Eisenstein series 80 20 60

Trace form

\( 90 q + 11 q^{2} - 19 q^{4} + 7 q^{5} - 5 q^{7} + 8 q^{8} + O(q^{10}) \) \( 90 q + 11 q^{2} - 19 q^{4} + 7 q^{5} - 5 q^{7} + 8 q^{8} - 7 q^{10} + 17 q^{11} - 11 q^{13} + 3 q^{14} - 39 q^{16} - 22 q^{19} - 43 q^{20} - 30 q^{22} - 8 q^{23} - 36 q^{25} - 33 q^{28} - 4 q^{29} - 22 q^{31} + 3 q^{32} - 7 q^{34} + 5 q^{35} + 37 q^{37} - 50 q^{38} - 51 q^{40} - 11 q^{41} + 45 q^{43} - 16 q^{44} + 75 q^{46} - 30 q^{47} - 66 q^{49} - 62 q^{50} + 96 q^{52} - 37 q^{53} + 51 q^{55} + 8 q^{56} - 11 q^{58} + 33 q^{59} + 27 q^{61} + 116 q^{62} + 120 q^{64} + 62 q^{65} - 15 q^{67} + 122 q^{68} + 78 q^{70} + 78 q^{71} - q^{73} + 64 q^{74} + 48 q^{76} + 6 q^{77} - 15 q^{79} + 42 q^{80} - 48 q^{82} - 2 q^{83} - 143 q^{85} - 37 q^{86} - 125 q^{88} - 81 q^{89} - 108 q^{91} - 82 q^{92} - 135 q^{94} - 84 q^{95} - 90 q^{97} - 133 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.2.i.a 207.i 23.c $10$ $1.653$ \(\Q(\zeta_{22})\) None \(-4\) \(0\) \(3\) \(6\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
207.2.i.b 207.i 23.c $10$ $1.653$ \(\Q(\zeta_{22})\) None \(4\) \(0\) \(-5\) \(-8\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots\)
207.2.i.c 207.i 23.c $10$ $1.653$ \(\Q(\zeta_{22})\) None \(7\) \(0\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1-\zeta_{22}-\zeta_{22}^{7}+\zeta_{22}^{8})q^{2}+(1+\cdots)q^{4}+\cdots\)
207.2.i.d 207.i 23.c $20$ $1.653$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(4\) \(0\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}-2\beta _{6}-2\beta _{7}+\cdots)q^{2}+\cdots\)
207.2.i.e 207.i 23.c $40$ $1.653$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)