Properties

Label 98.10.g
Level $98$
Weight $10$
Character orbit 98.g
Rep. character $\chi_{98}(9,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $504$
Newform subspaces $2$
Sturm bound $140$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 98.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(140\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(98, [\chi])\).

Total New Old
Modular forms 1536 504 1032
Cusp forms 1488 504 984
Eisenstein series 48 0 48

Trace form

\( 504 q + 162 q^{3} + 10752 q^{4} + 1818 q^{5} + 6176 q^{6} + 1784 q^{7} + 140378 q^{9} + O(q^{10}) \) \( 504 q + 162 q^{3} + 10752 q^{4} + 1818 q^{5} + 6176 q^{6} + 1784 q^{7} + 140378 q^{9} - 5632 q^{10} - 31794 q^{11} + 41472 q^{12} - 233176 q^{13} + 99072 q^{14} + 338142 q^{15} + 2752512 q^{16} + 2399122 q^{17} + 233408 q^{18} - 2667152 q^{19} + 87040 q^{20} - 365650 q^{21} + 5582752 q^{22} + 14055454 q^{23} + 1245184 q^{24} + 18020296 q^{25} + 3964192 q^{26} - 22193448 q^{27} - 3433984 q^{28} + 284522 q^{29} + 7471744 q^{30} + 16032506 q^{31} + 7030126 q^{33} - 10477568 q^{34} - 6485276 q^{35} - 162717184 q^{36} - 116601156 q^{37} - 35653952 q^{38} + 142314326 q^{39} + 90423296 q^{40} + 20817848 q^{41} - 29813408 q^{42} + 157629416 q^{43} - 96649728 q^{44} + 6800140 q^{45} + 101639104 q^{46} + 330555080 q^{47} + 127401984 q^{48} + 351824052 q^{49} - 37785216 q^{50} - 275665530 q^{51} - 299530240 q^{52} - 1170004486 q^{53} - 501508544 q^{54} - 956453264 q^{55} + 67354624 q^{56} + 737681532 q^{57} + 1319024448 q^{58} + 731332020 q^{59} - 95101440 q^{60} - 2072049280 q^{61} - 733516352 q^{62} + 646881864 q^{63} - 1409286144 q^{64} - 75525016 q^{65} - 232417280 q^{66} + 229617374 q^{67} - 525486592 q^{68} + 378190320 q^{69} + 179015200 q^{70} + 1311500652 q^{71} + 59752448 q^{72} - 844031318 q^{73} + 60244576 q^{74} + 959221076 q^{75} + 431440896 q^{76} + 2576482398 q^{77} + 1265799808 q^{78} - 458920182 q^{79} - 454295552 q^{80} - 2751928312 q^{81} + 541421568 q^{82} + 1717740624 q^{83} - 94641664 q^{84} + 2942443308 q^{85} - 1534917216 q^{86} - 1432199850 q^{87} - 1023877120 q^{88} + 3050788258 q^{89} + 3166358368 q^{90} - 7777530638 q^{91} - 1105126400 q^{92} - 10005075710 q^{93} + 3263764128 q^{94} + 4911565470 q^{95} + 318767104 q^{96} + 172025244 q^{97} + 6894458432 q^{98} - 16515507568 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.10.g.a 98.g 49.g $252$ $50.474$ None \(-336\) \(-568\) \(1085\) \(6796\) $\mathrm{SU}(2)[C_{21}]$
98.10.g.b 98.g 49.g $252$ $50.474$ None \(336\) \(730\) \(733\) \(-5012\) $\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{10}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)