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Properties

Label 22.7.d
Level $22$
Weight $7$
Character orbit 22.d
Rep. character $\chi_{22}(7,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 22.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(22, [\chi])\).

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24 q + 52 q^{3} + 192 q^{4} - 368 q^{5} + 400 q^{6} + 720 q^{7} - 3814 q^{9} + O(q^{10}) \) \( 24 q + 52 q^{3} + 192 q^{4} - 368 q^{5} + 400 q^{6} + 720 q^{7} - 3814 q^{9} + 4366 q^{11} + 3456 q^{12} + 3600 q^{13} - 4288 q^{14} - 2148 q^{15} - 6144 q^{16} - 5880 q^{17} + 18400 q^{18} - 23850 q^{19} + 11776 q^{20} - 1056 q^{22} - 40096 q^{23} + 12800 q^{24} + 69978 q^{25} + 52224 q^{26} + 4222 q^{27} - 32640 q^{28} - 204800 q^{29} - 134160 q^{30} + 71568 q^{31} + 11242 q^{33} + 88896 q^{34} + 469520 q^{35} + 25728 q^{36} + 309120 q^{37} - 73392 q^{38} - 328640 q^{39} - 107520 q^{40} - 541660 q^{41} - 177760 q^{42} + 213888 q^{44} + 811664 q^{45} + 213120 q^{46} - 299820 q^{47} + 53248 q^{48} - 374658 q^{49} - 364480 q^{50} - 1347330 q^{51} - 291840 q^{52} + 612820 q^{53} + 440004 q^{55} + 70656 q^{56} + 1416050 q^{57} + 552576 q^{58} + 927550 q^{59} + 206336 q^{60} - 1184160 q^{61} - 226640 q^{62} - 921200 q^{63} + 196608 q^{64} + 128672 q^{66} - 515100 q^{67} - 188160 q^{68} + 957220 q^{69} + 207984 q^{70} + 217572 q^{71} - 896000 q^{72} - 590340 q^{73} - 610400 q^{74} - 2208402 q^{75} - 2221964 q^{77} + 3228512 q^{78} + 93240 q^{79} + 196608 q^{80} + 1034076 q^{81} + 312960 q^{82} + 4588350 q^{83} + 2357760 q^{84} + 4132920 q^{85} + 1057632 q^{86} - 772608 q^{88} - 4638852 q^{89} - 6535040 q^{90} - 3916044 q^{91} - 2350208 q^{92} - 556628 q^{93} - 2410800 q^{94} + 661320 q^{95} - 342342 q^{97} + 4890070 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.7.d.a 22.d 11.d $24$ $5.061$ None \(0\) \(52\) \(-368\) \(720\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{7}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)