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Properties

Label 207.4.i
Level $207$
Weight $4$
Character orbit 207.i
Rep. character $\chi_{207}(55,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $290$
Newform subspaces $4$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 207.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(207, [\chi])\).

Total New Old
Modular forms 760 310 450
Cusp forms 680 290 390
Eisenstein series 80 20 60

Trace form

\( 290 q + 7 q^{2} - 99 q^{4} + 3 q^{5} - 19 q^{7} + 8 q^{8} + O(q^{10}) \) \( 290 q + 7 q^{2} - 99 q^{4} + 3 q^{5} - 19 q^{7} + 8 q^{8} - 73 q^{10} + 53 q^{11} + 31 q^{13} + 39 q^{14} - 835 q^{16} + 37 q^{17} + 73 q^{19} + 243 q^{20} + 574 q^{22} + 426 q^{23} - 402 q^{25} - 180 q^{26} + 19 q^{28} - 407 q^{29} - 567 q^{31} - 1233 q^{32} + 1701 q^{34} - 1219 q^{35} + 1209 q^{37} + 98 q^{38} + 1251 q^{40} - 205 q^{41} - 1481 q^{43} + 3304 q^{44} - 3879 q^{46} + 1248 q^{47} + 770 q^{49} + 1436 q^{50} - 296 q^{52} + 973 q^{53} + 5797 q^{55} + 1178 q^{56} + 421 q^{58} - 1527 q^{59} + 621 q^{61} - 2332 q^{62} - 5486 q^{64} - 2465 q^{65} + 51 q^{67} - 5826 q^{68} - 6354 q^{70} - 2257 q^{71} + 531 q^{73} - 3040 q^{74} - 9982 q^{76} - 5645 q^{77} - 2895 q^{79} - 3110 q^{80} + 5082 q^{82} + 7647 q^{83} + 10571 q^{85} + 11255 q^{86} + 7913 q^{88} + 7679 q^{89} + 6998 q^{91} + 8468 q^{92} + 9083 q^{94} + 909 q^{95} - 3235 q^{97} - 1661 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.4.i.a 207.i 23.c $50$ $12.213$ None 23.4.c.a \(11\) \(0\) \(19\) \(-19\) $\mathrm{SU}(2)[C_{11}]$
207.4.i.b 207.i 23.c $60$ $12.213$ None 69.4.e.b \(-4\) \(0\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{11}]$
207.4.i.c 207.i 23.c $60$ $12.213$ None 69.4.e.a \(0\) \(0\) \(-22\) \(24\) $\mathrm{SU}(2)[C_{11}]$
207.4.i.d 207.i 23.c $120$ $12.213$ None 207.4.i.d \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(207, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)