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Properties

Label 75.22.i
Level $75$
Weight $22$
Character orbit 75.i
Rep. character $\chi_{75}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $416$
Sturm bound $220$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 75.i (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(220\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(75, [\chi])\).

Total New Old
Modular forms 848 416 432
Cusp forms 832 416 416
Eisenstein series 16 0 16

Trace form

\( 416 q + 106954752 q^{4} - 24944730 q^{5} + 120932352 q^{6} + 27188753970 q^{8} + 362625577704 q^{9} + O(q^{10}) \) \( 416 q + 106954752 q^{4} - 24944730 q^{5} + 120932352 q^{6} + 27188753970 q^{8} + 362625577704 q^{9} + 1467444110 q^{10} - 143491984356 q^{11} + 4395431113788 q^{14} - 2367628113510 q^{15} - 107066185998860 q^{16} - 29164241554240 q^{17} - 5661170804852 q^{19} - 47560588967060 q^{20} + 66719523912804 q^{21} - 1301204528459030 q^{22} + 1199679605072480 q^{23} + 1521681143169024 q^{24} + 979058590378840 q^{25} - 1194268603963188 q^{26} - 2703567586590720 q^{28} - 11660269884658084 q^{29} - 7908570148265100 q^{30} + 11411130082327806 q^{31} + 24607736254697760 q^{33} - 4001625712522736 q^{34} + 3025494719806760 q^{35} - 372928160886423552 q^{36} + 22349919279682490 q^{37} - 168177628554886470 q^{38} - 65123248681532808 q^{39} + 287496808705500240 q^{40} + 447664223956021436 q^{41} - 433600892850677760 q^{42} - 719659185882650174 q^{44} + 86976895451156730 q^{45} + 175408305741618716 q^{46} - 2121874151960947960 q^{47} - 29963398690007271900 q^{49} + 181655511531408820 q^{50} - 3809357562483616032 q^{51} - 1223006229169863960 q^{52} + 8005333060257169010 q^{53} - 421665038529841152 q^{54} - 5926419300790708820 q^{55} + 21297348618757618500 q^{56} + 23458127922496273510 q^{58} - 16043351893772732688 q^{59} - 30753703161801585990 q^{60} - 15007734352890091200 q^{61} + 47367671559554917990 q^{62} - 11905689005897662260 q^{63} + 130550233377825377658 q^{64} + 106311495594106672210 q^{65} + 42209628310633543416 q^{66} - 39723479435432517540 q^{67} - 21697130162878457112 q^{69} - 58551694493233071720 q^{70} - 14907063700426739608 q^{71} + 94801323225222821970 q^{72} - 14830939412193392520 q^{73} - 285624264807366572852 q^{74} - 110232810228825964800 q^{75} - 558825902152380976032 q^{76} + 220589878548593212960 q^{77} - 34129637731450983520 q^{79} - 734236820229361105020 q^{80} - 1264397207741920595304 q^{81} - 1315555088910761453740 q^{83} + 589905062264568312 q^{84} + 507544510832524158410 q^{85} - 657147958412263059636 q^{86} - 663663222536771775960 q^{87} + 5391315432764919599710 q^{88} + 1455582852967522518018 q^{89} - 692644004257210432380 q^{90} + 1229579749731684663676 q^{91} + 5349201288811617259010 q^{92} - 2811774597747390140738 q^{94} + 3868789565046861055780 q^{95} - 1053489158840783119176 q^{96} - 545623839747703128210 q^{97} + 8433136123462077555060 q^{98} - 333550408480691220504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{22}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{22}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)