Properties

Label 930.2.bt.b
Level $930$
Weight $2$
Character orbit 930.bt
Analytic conductor $7.426$
Analytic rank $0$
Dimension $256$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bt (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(16\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 256q + 16q^{7} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 256q + 16q^{7} + 4q^{10} + 24q^{14} + 8q^{15} + 64q^{16} - 36q^{17} + 40q^{19} - 12q^{20} - 16q^{21} + 44q^{22} + 32q^{24} - 28q^{25} - 8q^{28} + 16q^{29} - 8q^{31} - 4q^{33} - 24q^{35} + 128q^{36} - 76q^{37} + 28q^{38} + 48q^{41} - 4q^{42} + 120q^{43} - 4q^{44} + 12q^{45} - 20q^{46} + 72q^{47} + 40q^{49} + 48q^{50} - 16q^{53} - 64q^{54} + 36q^{55} - 4q^{57} - 68q^{58} + 24q^{59} - 20q^{62} + 4q^{63} + 156q^{65} + 12q^{66} + 44q^{67} + 4q^{68} - 12q^{69} + 104q^{70} - 48q^{71} - 84q^{73} - 68q^{74} - 48q^{75} + 48q^{76} - 124q^{77} + 56q^{79} - 32q^{81} + 16q^{82} - 112q^{83} + 132q^{85} + 24q^{86} + 32q^{87} + 52q^{88} + 224q^{89} + 40q^{91} + 64q^{93} - 204q^{95} + 8q^{97} - 32q^{98} - 4q^{99} + O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
13.1 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −2.21414 + 0.312392i −0.866025 0.500000i −3.70934 0.194398i 0.453990 0.891007i −0.743145 0.669131i 0.0378215 2.23575i
13.2 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −1.71365 1.43646i −0.866025 0.500000i 1.75333 + 0.0918879i 0.453990 0.891007i −0.743145 0.669131i 1.68685 1.46784i
13.3 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −1.61201 + 1.54966i −0.866025 0.500000i 2.94133 + 0.154149i 0.453990 0.891007i −0.743145 0.669131i −1.27840 1.83458i
13.4 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i −0.0175372 2.23600i −0.866025 0.500000i −1.63070 0.0854612i 0.453990 0.891007i −0.743145 0.669131i 2.21121 + 0.332466i
13.5 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 0.0430415 2.23565i −0.866025 0.500000i 3.43163 + 0.179844i 0.453990 0.891007i −0.743145 0.669131i 2.20140 + 0.392245i
13.6 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 0.402123 + 2.19961i −0.866025 0.500000i −0.877389 0.0459820i 0.453990 0.891007i −0.743145 0.669131i −2.23544 + 0.0530771i
13.7 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 1.76804 + 1.36895i −0.866025 0.500000i 3.85109 + 0.201827i 0.453990 0.891007i −0.743145 0.669131i −1.62868 + 1.53213i
13.8 −0.156434 + 0.987688i −0.358368 + 0.933580i −0.951057 0.309017i 2.09871 0.771623i −0.866025 0.500000i −0.699531 0.0366609i 0.453990 0.891007i −0.743145 0.669131i 0.433812 + 2.19358i
13.9 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −2.22514 + 0.220752i −0.866025 0.500000i −2.35743 0.123548i −0.453990 + 0.891007i −0.743145 0.669131i −0.130055 + 2.23228i
13.10 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −1.14184 + 1.92255i −0.866025 0.500000i −0.0309572 0.00162240i −0.453990 + 0.891007i −0.743145 0.669131i 1.72026 + 1.42854i
13.11 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −0.657500 2.13722i −0.866025 0.500000i −3.81046 0.199698i −0.453990 + 0.891007i −0.743145 0.669131i −2.21376 + 0.315071i
13.12 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −0.322096 2.21275i −0.866025 0.500000i 3.31662 + 0.173817i −0.453990 + 0.891007i −0.743145 0.669131i −2.23589 0.0280193i
13.13 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i −0.285666 + 2.21775i −0.866025 0.500000i 2.60023 + 0.136272i −0.453990 + 0.891007i −0.743145 0.669131i 2.14575 + 0.629081i
13.14 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i 1.23620 + 1.86328i −0.866025 0.500000i −0.503455 0.0263849i −0.453990 + 0.891007i −0.743145 0.669131i 2.03372 0.929500i
13.15 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i 1.65605 1.50249i −0.866025 0.500000i −3.28823 0.172329i −0.453990 + 0.891007i −0.743145 0.669131i −1.22493 1.87071i
13.16 0.156434 0.987688i 0.358368 0.933580i −0.951057 0.309017i 2.17193 0.531716i −0.866025 0.500000i 1.18884 + 0.0623043i −0.453990 + 0.891007i −0.743145 0.669131i −0.185405 2.22837i
43.1 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −2.16210 0.570360i 0.866025 0.500000i −0.231757 4.42218i −0.891007 + 0.453990i 0.743145 0.669131i 2.22471 + 0.225111i
43.2 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −1.11506 + 1.93820i 0.866025 0.500000i −0.000384319 0.00733325i −0.891007 + 0.453990i 0.743145 0.669131i 0.798131 2.08878i
43.3 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −0.873557 2.05837i 0.866025 0.500000i 0.239568 + 4.57122i −0.891007 + 0.453990i 0.743145 0.669131i 1.18480 + 1.89638i
43.4 −0.987688 + 0.156434i −0.933580 + 0.358368i 0.951057 0.309017i −0.437784 + 2.19279i 0.866025 0.500000i 0.0914165 + 1.74433i −0.891007 + 0.453990i 0.743145 0.669131i 0.0893656 2.23428i
See next 80 embeddings (of 256 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 823.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
155.x even 60 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 930.2.bt.b yes 256
5.c odd 4 1 930.2.bt.a 256
31.h odd 30 1 930.2.bt.a 256
155.x even 60 1 inner 930.2.bt.b yes 256
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.bt.a 256 5.c odd 4 1
930.2.bt.a 256 31.h odd 30 1
930.2.bt.b yes 256 1.a even 1 1 trivial
930.2.bt.b yes 256 155.x even 60 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(14\!\cdots\!52\)\( T_{7}^{238} - \)\(80\!\cdots\!56\)\( T_{7}^{237} + \)\(10\!\cdots\!18\)\( T_{7}^{236} + \)\(19\!\cdots\!60\)\( T_{7}^{235} - \)\(14\!\cdots\!32\)\( T_{7}^{234} + \)\(91\!\cdots\!36\)\( T_{7}^{233} + \)\(39\!\cdots\!71\)\( T_{7}^{232} + \)\(14\!\cdots\!60\)\( T_{7}^{231} - \)\(21\!\cdots\!54\)\( T_{7}^{230} + \)\(12\!\cdots\!12\)\( T_{7}^{229} - \)\(13\!\cdots\!73\)\( T_{7}^{228} + \)\(41\!\cdots\!44\)\( T_{7}^{227} + \)\(21\!\cdots\!10\)\( T_{7}^{226} + \)\(61\!\cdots\!44\)\( T_{7}^{225} - \)\(91\!\cdots\!66\)\( T_{7}^{224} - \)\(68\!\cdots\!12\)\( T_{7}^{223} + \)\(16\!\cdots\!50\)\( T_{7}^{222} + \)\(15\!\cdots\!92\)\( T_{7}^{221} - \)\(25\!\cdots\!95\)\( T_{7}^{220} - \)\(56\!\cdots\!04\)\( T_{7}^{219} + \)\(36\!\cdots\!46\)\( T_{7}^{218} + \)\(92\!\cdots\!00\)\( T_{7}^{217} - \)\(10\!\cdots\!33\)\( T_{7}^{216} - \)\(30\!\cdots\!24\)\( T_{7}^{215} - \)\(19\!\cdots\!66\)\( T_{7}^{214} + \)\(28\!\cdots\!24\)\( T_{7}^{213} + \)\(18\!\cdots\!37\)\( T_{7}^{212} - \)\(43\!\cdots\!04\)\( T_{7}^{211} - \)\(54\!\cdots\!10\)\( T_{7}^{210} + \)\(12\!\cdots\!32\)\( T_{7}^{209} + \)\(11\!\cdots\!16\)\( T_{7}^{208} + \)\(40\!\cdots\!32\)\( T_{7}^{207} - \)\(23\!\cdots\!98\)\( T_{7}^{206} - \)\(11\!\cdots\!52\)\( T_{7}^{205} + \)\(35\!\cdots\!39\)\( T_{7}^{204} + \)\(29\!\cdots\!88\)\( T_{7}^{203} - \)\(51\!\cdots\!36\)\( T_{7}^{202} - \)\(51\!\cdots\!40\)\( T_{7}^{201} + \)\(61\!\cdots\!61\)\( T_{7}^{200} + \)\(11\!\cdots\!72\)\( T_{7}^{199} - \)\(61\!\cdots\!38\)\( T_{7}^{198} - \)\(16\!\cdots\!16\)\( T_{7}^{197} + \)\(52\!\cdots\!57\)\( T_{7}^{196} + \)\(27\!\cdots\!56\)\( T_{7}^{195} + \)\(67\!\cdots\!20\)\( T_{7}^{194} - \)\(32\!\cdots\!32\)\( T_{7}^{193} - \)\(95\!\cdots\!78\)\( T_{7}^{192} + \)\(49\!\cdots\!20\)\( T_{7}^{191} + \)\(28\!\cdots\!64\)\( T_{7}^{190} - \)\(72\!\cdots\!24\)\( T_{7}^{189} - \)\(53\!\cdots\!76\)\( T_{7}^{188} + \)\(11\!\cdots\!68\)\( T_{7}^{187} + \)\(82\!\cdots\!20\)\( T_{7}^{186} - \)\(19\!\cdots\!48\)\( T_{7}^{185} - \)\(11\!\cdots\!71\)\( T_{7}^{184} + \)\(25\!\cdots\!60\)\( T_{7}^{183} + \)\(12\!\cdots\!46\)\( T_{7}^{182} - \)\(37\!\cdots\!32\)\( T_{7}^{181} - \)\(13\!\cdots\!17\)\( T_{7}^{180} + \)\(39\!\cdots\!36\)\( T_{7}^{179} + \)\(11\!\cdots\!12\)\( T_{7}^{178} - \)\(41\!\cdots\!44\)\( T_{7}^{177} - \)\(89\!\cdots\!41\)\( T_{7}^{176} + \)\(38\!\cdots\!28\)\( T_{7}^{175} + \)\(78\!\cdots\!54\)\( T_{7}^{174} - \)\(18\!\cdots\!20\)\( T_{7}^{173} - \)\(17\!\cdots\!29\)\( T_{7}^{172} + \)\(19\!\cdots\!32\)\( T_{7}^{171} + \)\(49\!\cdots\!80\)\( T_{7}^{170} + \)\(85\!\cdots\!60\)\( T_{7}^{169} + \)\(68\!\cdots\!87\)\( T_{7}^{168} - \)\(86\!\cdots\!44\)\( T_{7}^{167} + \)\(19\!\cdots\!40\)\( T_{7}^{166} + \)\(90\!\cdots\!68\)\( T_{7}^{165} - \)\(38\!\cdots\!64\)\( T_{7}^{164} - \)\(29\!\cdots\!44\)\( T_{7}^{163} - \)\(49\!\cdots\!80\)\( T_{7}^{162} - \)\(31\!\cdots\!44\)\( T_{7}^{161} - \)\(41\!\cdots\!61\)\( T_{7}^{160} - \)\(21\!\cdots\!72\)\( T_{7}^{159} - \)\(30\!\cdots\!38\)\( T_{7}^{158} + \)\(34\!\cdots\!16\)\( T_{7}^{157} + \)\(24\!\cdots\!09\)\( T_{7}^{156} + \)\(79\!\cdots\!80\)\( T_{7}^{155} + \)\(36\!\cdots\!94\)\( T_{7}^{154} + \)\(16\!\cdots\!92\)\( T_{7}^{153} + \)\(63\!\cdots\!13\)\( T_{7}^{152} + \)\(18\!\cdots\!32\)\( T_{7}^{151} + \)\(39\!\cdots\!58\)\( T_{7}^{150} + \)\(66\!\cdots\!56\)\( T_{7}^{149} + \)\(10\!\cdots\!69\)\( T_{7}^{148} - \)\(51\!\cdots\!60\)\( T_{7}^{147} - \)\(19\!\cdots\!62\)\( T_{7}^{146} - \)\(10\!\cdots\!60\)\( T_{7}^{145} - \)\(34\!\cdots\!58\)\( T_{7}^{144} - \)\(94\!\cdots\!44\)\( T_{7}^{143} - \)\(24\!\cdots\!86\)\( T_{7}^{142} - \)\(60\!\cdots\!36\)\( T_{7}^{141} - \)\(11\!\cdots\!51\)\( T_{7}^{140} - \)\(91\!\cdots\!00\)\( T_{7}^{139} + \)\(40\!\cdots\!88\)\( T_{7}^{138} + \)\(21\!\cdots\!12\)\( T_{7}^{137} + \)\(69\!\cdots\!68\)\( T_{7}^{136} + \)\(19\!\cdots\!40\)\( T_{7}^{135} + \)\(56\!\cdots\!10\)\( T_{7}^{134} + \)\(14\!\cdots\!60\)\( T_{7}^{133} + \)\(24\!\cdots\!41\)\( T_{7}^{132} + \)\(16\!\cdots\!08\)\( T_{7}^{131} - \)\(20\!\cdots\!16\)\( T_{7}^{130} + \)\(33\!\cdots\!80\)\( T_{7}^{129} + \)\(60\!\cdots\!59\)\( T_{7}^{128} + \)\(25\!\cdots\!64\)\( T_{7}^{127} + \)\(79\!\cdots\!96\)\( T_{7}^{126} + \)\(26\!\cdots\!88\)\( T_{7}^{125} + \)\(88\!\cdots\!88\)\( T_{7}^{124} + \)\(21\!\cdots\!92\)\( T_{7}^{123} + \)\(25\!\cdots\!42\)\( T_{7}^{122} - \)\(70\!\cdots\!88\)\( T_{7}^{121} - \)\(50\!\cdots\!13\)\( T_{7}^{120} - \)\(17\!\cdots\!84\)\( T_{7}^{119} - \)\(48\!\cdots\!62\)\( T_{7}^{118} - \)\(12\!\cdots\!24\)\( T_{7}^{117} - \)\(32\!\cdots\!45\)\( T_{7}^{116} - \)\(71\!\cdots\!64\)\( T_{7}^{115} - \)\(10\!\cdots\!88\)\( T_{7}^{114} - \)\(93\!\cdots\!16\)\( T_{7}^{113} + \)\(57\!\cdots\!25\)\( T_{7}^{112} + \)\(22\!\cdots\!24\)\( T_{7}^{111} + \)\(62\!\cdots\!00\)\( T_{7}^{110} + \)\(14\!\cdots\!72\)\( T_{7}^{109} + \)\(32\!\cdots\!88\)\( T_{7}^{108} + \)\(64\!\cdots\!44\)\( T_{7}^{107} + \)\(91\!\cdots\!74\)\( T_{7}^{106} + \)\(23\!\cdots\!60\)\( T_{7}^{105} - \)\(32\!\cdots\!69\)\( T_{7}^{104} - \)\(97\!\cdots\!36\)\( T_{7}^{103} - \)\(10\!\cdots\!70\)\( T_{7}^{102} + \)\(23\!\cdots\!76\)\( T_{7}^{101} + \)\(14\!\cdots\!23\)\( T_{7}^{100} + \)\(36\!\cdots\!88\)\( T_{7}^{99} + \)\(58\!\cdots\!04\)\( T_{7}^{98} + \)\(42\!\cdots\!44\)\( T_{7}^{97} - \)\(73\!\cdots\!88\)\( T_{7}^{96} - \)\(34\!\cdots\!16\)\( T_{7}^{95} - \)\(74\!\cdots\!04\)\( T_{7}^{94} - \)\(10\!\cdots\!68\)\( T_{7}^{93} - \)\(79\!\cdots\!24\)\( T_{7}^{92} + \)\(73\!\cdots\!52\)\( T_{7}^{91} + \)\(39\!\cdots\!94\)\( T_{7}^{90} + \)\(80\!\cdots\!84\)\( T_{7}^{89} + \)\(92\!\cdots\!89\)\( T_{7}^{88} - \)\(48\!\cdots\!24\)\( T_{7}^{87} - \)\(31\!\cdots\!62\)\( T_{7}^{86} - \)\(88\!\cdots\!72\)\( T_{7}^{85} - \)\(16\!\cdots\!81\)\( T_{7}^{84} - \)\(22\!\cdots\!36\)\( T_{7}^{83} - \)\(19\!\cdots\!94\)\( T_{7}^{82} + \)\(10\!\cdots\!28\)\( T_{7}^{81} + \)\(52\!\cdots\!00\)\( T_{7}^{80} + \)\(14\!\cdots\!24\)\( T_{7}^{79} + \)\(29\!\cdots\!80\)\( T_{7}^{78} + \)\(47\!\cdots\!28\)\( T_{7}^{77} + \)\(68\!\cdots\!68\)\( T_{7}^{76} + \)\(86\!\cdots\!24\)\( T_{7}^{75} + \)\(94\!\cdots\!04\)\( T_{7}^{74} + \)\(84\!\cdots\!36\)\( T_{7}^{73} + \)\(41\!\cdots\!77\)\( T_{7}^{72} - \)\(45\!\cdots\!64\)\( T_{7}^{71} - \)\(18\!\cdots\!56\)\( T_{7}^{70} - \)\(35\!\cdots\!08\)\( T_{7}^{69} - \)\(53\!\cdots\!76\)\( T_{7}^{68} - \)\(65\!\cdots\!08\)\( T_{7}^{67} - \)\(66\!\cdots\!98\)\( T_{7}^{66} - \)\(51\!\cdots\!84\)\( T_{7}^{65} - \)\(22\!\cdots\!58\)\( T_{7}^{64} + \)\(16\!\cdots\!64\)\( T_{7}^{63} + \)\(55\!\cdots\!92\)\( T_{7}^{62} + \)\(84\!\cdots\!00\)\( T_{7}^{61} + \)\(97\!\cdots\!94\)\( T_{7}^{60} + \)\(94\!\cdots\!92\)\( T_{7}^{59} + \)\(80\!\cdots\!12\)\( T_{7}^{58} + \)\(62\!\cdots\!16\)\( T_{7}^{57} + \)\(48\!\cdots\!12\)\( T_{7}^{56} + \)\(40\!\cdots\!16\)\( T_{7}^{55} + \)\(39\!\cdots\!58\)\( T_{7}^{54} + \)\(40\!\cdots\!08\)\( T_{7}^{53} + \)\(42\!\cdots\!83\)\( T_{7}^{52} + \)\(41\!\cdots\!48\)\( T_{7}^{51} + \)\(37\!\cdots\!82\)\( T_{7}^{50} + \)\(30\!\cdots\!00\)\( T_{7}^{49} + \)\(23\!\cdots\!75\)\( T_{7}^{48} + \)\(17\!\cdots\!80\)\( T_{7}^{47} + \)\(12\!\cdots\!22\)\( T_{7}^{46} + \)\(83\!\cdots\!36\)\( T_{7}^{45} + \)\(58\!\cdots\!75\)\( T_{7}^{44} + \)\(43\!\cdots\!24\)\( T_{7}^{43} + \)\(32\!\cdots\!88\)\( T_{7}^{42} + \)\(24\!\cdots\!40\)\( T_{7}^{41} + \)\(18\!\cdots\!96\)\( T_{7}^{40} + \)\(12\!\cdots\!16\)\( T_{7}^{39} + \)\(86\!\cdots\!74\)\( T_{7}^{38} + \)\(54\!\cdots\!08\)\( T_{7}^{37} + \)\(32\!\cdots\!21\)\( T_{7}^{36} + \)\(18\!\cdots\!08\)\( T_{7}^{35} + \)\(98\!\cdots\!34\)\( T_{7}^{34} + \)\(50\!\cdots\!56\)\( T_{7}^{33} + \)\(24\!\cdots\!89\)\( T_{7}^{32} + \)\(11\!\cdots\!44\)\( T_{7}^{31} + \)\(50\!\cdots\!40\)\( T_{7}^{30} + \)\(21\!\cdots\!24\)\( T_{7}^{29} + \)\(82\!\cdots\!84\)\( T_{7}^{28} + \)\(29\!\cdots\!00\)\( T_{7}^{27} + \)\(97\!\cdots\!12\)\( T_{7}^{26} + \)\(29\!\cdots\!92\)\( T_{7}^{25} + \)\(91\!\cdots\!04\)\( T_{7}^{24} + \)\(32\!\cdots\!64\)\( T_{7}^{23} + \)\(12\!\cdots\!64\)\( T_{7}^{22} + \)\(36\!\cdots\!60\)\( T_{7}^{21} + \)\(69\!\cdots\!08\)\( T_{7}^{20} + \)\(69\!\cdots\!40\)\( T_{7}^{19} + \)\(76\!\cdots\!04\)\( T_{7}^{18} + \)\(50\!\cdots\!92\)\( T_{7}^{17} + \)\(17\!\cdots\!56\)\( T_{7}^{16} + \)\(41\!\cdots\!12\)\( T_{7}^{15} + \)\(84\!\cdots\!76\)\( T_{7}^{14} - \)\(23\!\cdots\!76\)\( T_{7}^{13} - \)\(43\!\cdots\!84\)\( T_{7}^{12} - \)\(31\!\cdots\!84\)\( T_{7}^{11} + \)\(54\!\cdots\!44\)\( T_{7}^{10} + \)\(75\!\cdots\!00\)\( T_{7}^{9} + \)\(21\!\cdots\!52\)\( T_{7}^{8} + \)\(20\!\cdots\!24\)\( T_{7}^{7} + \)\(10\!\cdots\!60\)\( T_{7}^{6} + \)\(58\!\cdots\!36\)\( T_{7}^{5} + \)\(58\!\cdots\!80\)\( T_{7}^{4} + \)\(26\!\cdots\!80\)\( T_{7}^{3} + \)\(40\!\cdots\!84\)\( T_{7}^{2} + \)\(16\!\cdots\!92\)\( T_{7} + \)\(18\!\cdots\!36\)\( \)">\(T_{7}^{256} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(930, [\chi])\).