Newspace parameters
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
26.1 | −4.69077 | − | 2.70822i | 2.33527 | + | 4.64182i | 10.6689 | + | 18.4790i | 2.50000 | − | 4.33013i | 1.61684 | − | 28.0981i | 14.5222 | + | 11.4937i | − | 72.2429i | −16.0930 | + | 21.6798i | −23.4538 | + | 13.5411i | |
26.2 | −3.95258 | − | 2.28202i | −1.04959 | − | 5.08904i | 6.41528 | + | 11.1116i | 2.50000 | − | 4.33013i | −7.46472 | + | 22.5101i | −15.3726 | − | 10.3287i | − | 22.0469i | −24.7967 | + | 10.6828i | −19.7629 | + | 11.4101i | |
26.3 | −3.64936 | − | 2.10696i | 4.12131 | − | 3.16462i | 4.87855 | + | 8.44990i | 2.50000 | − | 4.33013i | −21.7079 | + | 2.86543i | 16.7999 | − | 7.79504i | − | 7.40430i | 6.97031 | − | 26.0848i | −18.2468 | + | 10.5348i | |
26.4 | −3.53626 | − | 2.04166i | −5.19608 | − | 0.0272697i | 4.33676 | + | 7.51148i | 2.50000 | − | 4.33013i | 18.3190 | + | 10.7051i | 0.627588 | + | 18.5096i | − | 2.75017i | 26.9985 | + | 0.283391i | −17.6813 | + | 10.2083i | |
26.5 | −2.43022 | − | 1.40309i | 2.69612 | + | 4.44195i | −0.0626967 | − | 0.108594i | 2.50000 | − | 4.33013i | −0.319698 | − | 14.5778i | −12.1846 | − | 13.9476i | 22.8013i | −12.4619 | + | 23.9520i | −12.1511 | + | 7.01543i | ||
26.6 | −1.48940 | − | 0.859905i | −4.80226 | + | 1.98451i | −2.52113 | − | 4.36672i | 2.50000 | − | 4.33013i | 8.85898 | + | 1.17376i | 2.28179 | − | 18.3792i | 22.4302i | 19.1235 | − | 19.0603i | −7.44700 | + | 4.29953i | ||
26.7 | −0.815639 | − | 0.470909i | −0.600797 | + | 5.16130i | −3.55649 | − | 6.16002i | 2.50000 | − | 4.33013i | 2.92054 | − | 3.92684i | 13.9941 | + | 12.1312i | 14.2337i | −26.2781 | − | 6.20179i | −4.07820 | + | 2.35455i | ||
26.8 | −0.155491 | − | 0.0897728i | 2.14006 | − | 4.73499i | −3.98388 | − | 6.90029i | 2.50000 | − | 4.33013i | −0.757834 | + | 0.544130i | 18.1774 | + | 3.54688i | 2.86694i | −17.8403 | − | 20.2663i | −0.777456 | + | 0.448864i | ||
26.9 | 0.133140 | + | 0.0768685i | −2.72308 | − | 4.42548i | −3.98818 | − | 6.90773i | 2.50000 | − | 4.33013i | −0.0223714 | − | 0.798528i | −15.0457 | + | 10.7995i | − | 2.45616i | −12.1697 | + | 24.1018i | 0.665701 | − | 0.384343i | |
26.10 | 1.20225 | + | 0.694119i | 5.16393 | − | 0.577779i | −3.03640 | − | 5.25919i | 2.50000 | − | 4.33013i | 6.60938 | + | 2.88975i | −11.1211 | − | 14.8095i | − | 19.5364i | 26.3323 | − | 5.96722i | 6.01125 | − | 3.47060i | |
26.11 | 1.35336 | + | 0.781362i | −2.92325 | + | 4.29588i | −2.77895 | − | 4.81328i | 2.50000 | − | 4.33013i | −7.31285 | + | 3.52975i | −17.7664 | + | 5.23007i | − | 21.1872i | −9.90921 | − | 25.1159i | 6.76679 | − | 3.90681i | |
26.12 | 2.51429 | + | 1.45163i | −5.18226 | − | 0.379674i | 0.214449 | + | 0.371437i | 2.50000 | − | 4.33013i | −12.4786 | − | 8.47733i | 17.9959 | + | 4.37591i | − | 21.9809i | 26.7117 | + | 3.93514i | 12.5715 | − | 7.25814i | |
26.13 | 3.06378 | + | 1.76887i | 4.26753 | + | 2.96449i | 2.25781 | + | 3.91065i | 2.50000 | − | 4.33013i | 7.83096 | + | 16.6312i | 5.77785 | + | 17.5959i | − | 12.3268i | 9.42363 | + | 25.3021i | 15.3189 | − | 8.84436i | |
26.14 | 3.31734 | + | 1.91526i | −0.144315 | − | 5.19415i | 3.33648 | + | 5.77895i | 2.50000 | − | 4.33013i | 9.46943 | − | 17.5071i | 8.94735 | − | 16.2156i | − | 5.08329i | −26.9583 | + | 1.49918i | 16.5867 | − | 9.57632i | |
26.15 | 4.56345 | + | 2.63471i | −1.17580 | + | 5.06137i | 9.88336 | + | 17.1185i | 2.50000 | − | 4.33013i | −18.7009 | + | 19.9994i | 12.9395 | − | 13.2503i | 62.0037i | −24.2350 | − | 11.9023i | 22.8172 | − | 13.1735i | ||
26.16 | 4.57212 | + | 2.63971i | 4.07322 | − | 3.22628i | 9.93617 | + | 17.2100i | 2.50000 | − | 4.33013i | 27.1397 | − | 3.99877i | −17.5731 | + | 5.84690i | 62.6791i | 6.18230 | − | 26.2827i | 22.8606 | − | 13.1986i | ||
101.1 | −4.69077 | + | 2.70822i | 2.33527 | − | 4.64182i | 10.6689 | − | 18.4790i | 2.50000 | + | 4.33013i | 1.61684 | + | 28.0981i | 14.5222 | − | 11.4937i | 72.2429i | −16.0930 | − | 21.6798i | −23.4538 | − | 13.5411i | ||
101.2 | −3.95258 | + | 2.28202i | −1.04959 | + | 5.08904i | 6.41528 | − | 11.1116i | 2.50000 | + | 4.33013i | −7.46472 | − | 22.5101i | −15.3726 | + | 10.3287i | 22.0469i | −24.7967 | − | 10.6828i | −19.7629 | − | 11.4101i | ||
101.3 | −3.64936 | + | 2.10696i | 4.12131 | + | 3.16462i | 4.87855 | − | 8.44990i | 2.50000 | + | 4.33013i | −21.7079 | − | 2.86543i | 16.7999 | + | 7.79504i | 7.40430i | 6.97031 | + | 26.0848i | −18.2468 | − | 10.5348i | ||
101.4 | −3.53626 | + | 2.04166i | −5.19608 | + | 0.0272697i | 4.33676 | − | 7.51148i | 2.50000 | + | 4.33013i | 18.3190 | − | 10.7051i | 0.627588 | − | 18.5096i | 2.75017i | 26.9985 | − | 0.283391i | −17.6813 | − | 10.2083i | ||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
21.g | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 105.4.s.b | yes | 32 |
3.b | odd | 2 | 1 | 105.4.s.a | ✓ | 32 | |
7.d | odd | 6 | 1 | 105.4.s.a | ✓ | 32 | |
21.g | even | 6 | 1 | inner | 105.4.s.b | yes | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
105.4.s.a | ✓ | 32 | 3.b | odd | 2 | 1 | |
105.4.s.a | ✓ | 32 | 7.d | odd | 6 | 1 | |
105.4.s.b | yes | 32 | 1.a | even | 1 | 1 | trivial |
105.4.s.b | yes | 32 | 21.g | even | 6 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \(12\!\cdots\!44\)\( T_{2}^{14} + 335728806336 T_{2}^{13} + \)\(58\!\cdots\!84\)\( T_{2}^{12} - \)\(19\!\cdots\!28\)\( T_{2}^{11} - \)\(16\!\cdots\!24\)\( T_{2}^{10} + \)\(61\!\cdots\!80\)\( T_{2}^{9} + \)\(32\!\cdots\!68\)\( T_{2}^{8} - \)\(12\!\cdots\!88\)\( T_{2}^{7} - \)\(31\!\cdots\!72\)\( T_{2}^{6} + \)\(84\!\cdots\!40\)\( T_{2}^{5} + \)\(22\!\cdots\!40\)\( T_{2}^{4} + 714941199360 T_{2}^{3} - 602278336512 T_{2}^{2} - 18831605760 T_{2} + 16057958400 \)">\(T_{2}^{32} - \cdots\) acting on \(S_{4}^{\mathrm{new}}(105, [\chi])\).