Properties

Label 121.4.c
Level $121$
Weight $4$
Character orbit 121.c
Rep. character $\chi_{121}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $92$
Newform subspaces $10$
Sturm bound $44$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 10 \)
Sturm bound: \(44\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(121, [\chi])\).

Total New Old
Modular forms 156 124 32
Cusp forms 108 92 16
Eisenstein series 48 32 16

Trace form

\( 92 q + 7 q^{2} + 5 q^{3} - 83 q^{4} + 3 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} - 182 q^{9} + O(q^{10}) \) \( 92 q + 7 q^{2} + 5 q^{3} - 83 q^{4} + 3 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} - 182 q^{9} - 40 q^{10} - 358 q^{12} + 65 q^{13} + 248 q^{14} + 83 q^{15} + 245 q^{16} + 31 q^{17} + 102 q^{18} - 148 q^{19} - 426 q^{20} - 334 q^{21} + 52 q^{23} + 447 q^{24} + 148 q^{25} + 148 q^{26} - 166 q^{27} + 42 q^{28} + 199 q^{29} + 114 q^{30} + 369 q^{31} - 324 q^{32} + 530 q^{34} - 237 q^{35} - 26 q^{36} - 33 q^{37} + 290 q^{38} - 365 q^{39} - 532 q^{40} + 31 q^{41} + 294 q^{42} + 650 q^{43} - 1204 q^{45} - 1204 q^{46} - 1259 q^{47} - 254 q^{48} - 1110 q^{49} + 147 q^{50} + 246 q^{51} + 590 q^{52} + 1719 q^{53} + 3100 q^{54} + 2664 q^{56} - 102 q^{57} - 1048 q^{58} - 478 q^{59} - 400 q^{60} + 525 q^{61} - 2456 q^{62} + 68 q^{63} + 861 q^{64} - 1790 q^{65} - 806 q^{67} - 710 q^{68} - 228 q^{69} + 288 q^{70} - 1027 q^{71} - 919 q^{72} + 2155 q^{73} + 1476 q^{74} + 54 q^{75} + 242 q^{76} + 2716 q^{78} + 861 q^{79} + 3156 q^{80} + 1489 q^{81} + 3915 q^{82} - 52 q^{83} + 84 q^{84} - 2383 q^{85} - 1203 q^{86} - 2310 q^{87} - 5382 q^{89} + 1682 q^{90} - 3871 q^{91} + 1158 q^{92} - 2013 q^{93} - 702 q^{94} + 1317 q^{95} - 1252 q^{96} - 2094 q^{97} - 2740 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.4.c.a 121.c 11.c $4$ $7.139$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) 121.4.a.a \(0\) \(-8\) \(-18\) \(0\) $\mathrm{U}(1)[D_{5}]$ \(q+8\zeta_{10}^{2}q^{3}+8\zeta_{10}^{3}q^{4}-18\zeta_{10}q^{5}+\cdots\)
121.4.c.b 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).1 None 11.4.c.a \(-3\) \(-3\) \(18\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
121.4.c.c 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None 11.4.a.a \(-2\) \(2\) \(-2\) \(-20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{7})q^{2}+(-4\beta _{1}-\beta _{6})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.d 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None 121.4.a.b \(-2\) \(8\) \(10\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}-\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.e 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).7 None 121.4.a.d \(0\) \(10\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{7}q^{2}-5\beta _{6}q^{3}+18\beta _{4}q^{4}+(-5+\cdots)q^{5}+\cdots\)
121.4.c.f 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None 11.4.a.a \(2\) \(2\) \(-2\) \(20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{7})q^{2}+(4\beta _{1}-\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.g 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None 121.4.a.b \(2\) \(8\) \(10\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.h 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).1 None 11.4.c.a \(3\) \(-3\) \(18\) \(10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+2\beta _{4}+\beta _{6}-\beta _{7})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.i 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).1 None 11.4.c.a \(7\) \(-3\) \(-7\) \(35\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.j 121.c 11.c $24$ $7.139$ None 121.4.a.h \(0\) \(-8\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(121, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(121, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)