Properties

Label 4410.2.d
Level $4410$
Weight $2$
Character orbit 4410.d
Rep. character $\chi_{4410}(4409,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $4$
Sturm bound $2016$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4410.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(2016\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4410, [\chi])\).

Total New Old
Modular forms 1072 80 992
Cusp forms 944 80 864
Eisenstein series 128 0 128

Trace form

\( 80q + 80q^{4} + O(q^{10}) \) \( 80q + 80q^{4} + 80q^{16} - 8q^{25} - 32q^{46} + 80q^{64} - 16q^{79} + 64q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4410, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4410.2.d.a \(16\) \(35.214\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{5}q^{5}-q^{8}-\beta _{5}q^{10}+\cdots\)
4410.2.d.b \(16\) \(35.214\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+\beta _{10}q^{5}+q^{8}+\beta _{10}q^{10}+\cdots\)
4410.2.d.c \(24\) \(35.214\) None \(-24\) \(0\) \(0\) \(0\)
4410.2.d.d \(24\) \(35.214\) None \(24\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(4410, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4410, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2205, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T )^{16} \))(\( ( 1 - T )^{16} \))
$3$ 1
$5$ (\( 1 - 6 T^{2} + 17 T^{4} + 42 T^{6} - 876 T^{8} + 1050 T^{10} + 10625 T^{12} - 93750 T^{14} + 390625 T^{16} \))(\( 1 - 6 T^{2} + 17 T^{4} + 42 T^{6} - 876 T^{8} + 1050 T^{10} + 10625 T^{12} - 93750 T^{14} + 390625 T^{16} \))
$7$ 1
$11$ (\( ( 1 - 38 T^{2} + 514 T^{4} - 1376 T^{6} - 21281 T^{8} - 166496 T^{10} + 7525474 T^{12} - 67319318 T^{14} + 214358881 T^{16} )^{2} \))(\( ( 1 - 38 T^{2} + 514 T^{4} - 1376 T^{6} - 21281 T^{8} - 166496 T^{10} + 7525474 T^{12} - 67319318 T^{14} + 214358881 T^{16} )^{2} \))
$13$ (\( ( 1 + 32 T^{2} + 473 T^{4} + 8616 T^{6} + 148784 T^{8} + 1456104 T^{10} + 13509353 T^{12} + 154457888 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 + 32 T^{2} + 473 T^{4} + 8616 T^{6} + 148784 T^{8} + 1456104 T^{10} + 13509353 T^{12} + 154457888 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( ( 1 - 52 T^{2} + 1784 T^{4} - 42108 T^{6} + 805934 T^{8} - 12169212 T^{10} + 149001464 T^{12} - 1255153588 T^{14} + 6975757441 T^{16} )^{2} \))(\( ( 1 - 52 T^{2} + 1784 T^{4} - 42108 T^{6} + 805934 T^{8} - 12169212 T^{10} + 149001464 T^{12} - 1255153588 T^{14} + 6975757441 T^{16} )^{2} \))
$19$ (\( ( 1 - 42 T^{2} + 1613 T^{4} - 45630 T^{6} + 903912 T^{8} - 16472430 T^{10} + 210207773 T^{12} - 1975927002 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 42 T^{2} + 1613 T^{4} - 45630 T^{6} + 903912 T^{8} - 16472430 T^{10} + 210207773 T^{12} - 1975927002 T^{14} + 16983563041 T^{16} )^{2} \))
$23$ (\( ( 1 + 4 T + 39 T^{2} + 12 T^{3} + 442 T^{4} + 276 T^{5} + 20631 T^{6} + 48668 T^{7} + 279841 T^{8} )^{4} \))(\( ( 1 - 4 T + 39 T^{2} - 12 T^{3} + 442 T^{4} - 276 T^{5} + 20631 T^{6} - 48668 T^{7} + 279841 T^{8} )^{4} \))
$29$ (\( ( 1 - 110 T^{2} + 5617 T^{4} - 185030 T^{6} + 5268820 T^{8} - 155610230 T^{10} + 3972797377 T^{12} - 65430565310 T^{14} + 500246412961 T^{16} )^{2} \))(\( ( 1 - 110 T^{2} + 5617 T^{4} - 185030 T^{6} + 5268820 T^{8} - 155610230 T^{10} + 3972797377 T^{12} - 65430565310 T^{14} + 500246412961 T^{16} )^{2} \))
$31$ (\( ( 1 - 6 T^{2} + 1673 T^{4} - 1134 T^{6} + 1898388 T^{8} - 1089774 T^{10} + 1545050633 T^{12} - 5325022086 T^{14} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 6 T^{2} + 1673 T^{4} - 1134 T^{6} + 1898388 T^{8} - 1089774 T^{10} + 1545050633 T^{12} - 5325022086 T^{14} + 852891037441 T^{16} )^{2} \))
$37$ (\( ( 1 - 184 T^{2} + 15497 T^{4} - 826872 T^{6} + 33651488 T^{8} - 1131987768 T^{10} + 29043873017 T^{12} - 472093659256 T^{14} + 3512479453921 T^{16} )^{2} \))(\( ( 1 - 184 T^{2} + 15497 T^{4} - 826872 T^{6} + 33651488 T^{8} - 1131987768 T^{10} + 29043873017 T^{12} - 472093659256 T^{14} + 3512479453921 T^{16} )^{2} \))
$41$ (\( ( 1 + 84 T^{2} + 9077 T^{4} + 448128 T^{6} + 24944604 T^{8} + 753303168 T^{10} + 25649432597 T^{12} + 399008756244 T^{14} + 7984925229121 T^{16} )^{2} \))(\( ( 1 + 84 T^{2} + 9077 T^{4} + 448128 T^{6} + 24944604 T^{8} + 753303168 T^{10} + 25649432597 T^{12} + 399008756244 T^{14} + 7984925229121 T^{16} )^{2} \))
$43$ (\( ( 1 - 196 T^{2} + 20648 T^{4} - 1438284 T^{6} + 72218798 T^{8} - 2659387116 T^{10} + 70591403048 T^{12} - 1238987157604 T^{14} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 196 T^{2} + 20648 T^{4} - 1438284 T^{6} + 72218798 T^{8} - 2659387116 T^{10} + 70591403048 T^{12} - 1238987157604 T^{14} + 11688200277601 T^{16} )^{2} \))
$47$ (\( ( 1 - 270 T^{2} + 34853 T^{4} - 2827818 T^{6} + 158149800 T^{8} - 6246649962 T^{10} + 170071521893 T^{12} - 2910388138830 T^{14} + 23811286661761 T^{16} )^{2} \))(\( ( 1 - 270 T^{2} + 34853 T^{4} - 2827818 T^{6} + 158149800 T^{8} - 6246649962 T^{10} + 170071521893 T^{12} - 2910388138830 T^{14} + 23811286661761 T^{16} )^{2} \))
$53$ (\( ( 1 - 8 T + 168 T^{2} - 1044 T^{3} + 13021 T^{4} - 55332 T^{5} + 471912 T^{6} - 1191016 T^{7} + 7890481 T^{8} )^{4} \))(\( ( 1 + 8 T + 168 T^{2} + 1044 T^{3} + 13021 T^{4} + 55332 T^{5} + 471912 T^{6} + 1191016 T^{7} + 7890481 T^{8} )^{4} \))
$59$ (\( ( 1 + 426 T^{2} + 81485 T^{4} + 9169758 T^{6} + 665481384 T^{8} + 31919927598 T^{10} + 987383161085 T^{12} + 17968907331066 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 + 426 T^{2} + 81485 T^{4} + 9169758 T^{6} + 665481384 T^{8} + 31919927598 T^{10} + 987383161085 T^{12} + 17968907331066 T^{14} + 146830437604321 T^{16} )^{2} \))
$61$ (\( ( 1 - 68 T^{2} + 13144 T^{4} - 707276 T^{6} + 70076494 T^{8} - 2631773996 T^{10} + 181989734104 T^{12} - 3503385456548 T^{14} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 68 T^{2} + 13144 T^{4} - 707276 T^{6} + 70076494 T^{8} - 2631773996 T^{10} + 181989734104 T^{12} - 3503385456548 T^{14} + 191707312997281 T^{16} )^{2} \))
$67$ (\( ( 1 - 352 T^{2} + 61868 T^{4} - 7006944 T^{6} + 554935238 T^{8} - 31454171616 T^{10} + 1246709554028 T^{12} - 31841350523488 T^{14} + 406067677556641 T^{16} )^{2} \))(\( ( 1 - 352 T^{2} + 61868 T^{4} - 7006944 T^{6} + 554935238 T^{8} - 31454171616 T^{10} + 1246709554028 T^{12} - 31841350523488 T^{14} + 406067677556641 T^{16} )^{2} \))
$71$ (\( ( 1 + 52 T^{2} + 10456 T^{4} + 567388 T^{6} + 78505582 T^{8} + 2860202908 T^{10} + 265704536536 T^{12} + 6661214763892 T^{14} + 645753531245761 T^{16} )^{2} \))(\( ( 1 + 52 T^{2} + 10456 T^{4} + 567388 T^{6} + 78505582 T^{8} + 2860202908 T^{10} + 265704536536 T^{12} + 6661214763892 T^{14} + 645753531245761 T^{16} )^{2} \))
$73$ (\( ( 1 + 312 T^{2} + 51644 T^{4} + 5812104 T^{6} + 484685382 T^{8} + 30972702216 T^{10} + 1466598758204 T^{12} + 47216278602168 T^{14} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 312 T^{2} + 51644 T^{4} + 5812104 T^{6} + 484685382 T^{8} + 30972702216 T^{10} + 1466598758204 T^{12} + 47216278602168 T^{14} + 806460091894081 T^{16} )^{2} \))
$79$ (\( ( 1 + 2 T + 59 T^{2} + 870 T^{3} + 6116 T^{4} + 68730 T^{5} + 368219 T^{6} + 986078 T^{7} + 38950081 T^{8} )^{4} \))(\( ( 1 + 2 T + 59 T^{2} + 870 T^{3} + 6116 T^{4} + 68730 T^{5} + 368219 T^{6} + 986078 T^{7} + 38950081 T^{8} )^{4} \))
$83$ (\( ( 1 - 250 T^{2} + 32249 T^{4} - 3769146 T^{6} + 372693188 T^{8} - 25965646794 T^{10} + 1530483393929 T^{12} - 81735093342250 T^{14} + 2252292232139041 T^{16} )^{2} \))(\( ( 1 - 250 T^{2} + 32249 T^{4} - 3769146 T^{6} + 372693188 T^{8} - 25965646794 T^{10} + 1530483393929 T^{12} - 81735093342250 T^{14} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( ( 1 + 492 T^{2} + 112712 T^{4} + 16213956 T^{6} + 1669259214 T^{8} + 128430745476 T^{10} + 7071803467592 T^{12} + 244514795152812 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 492 T^{2} + 112712 T^{4} + 16213956 T^{6} + 1669259214 T^{8} + 128430745476 T^{10} + 7071803467592 T^{12} + 244514795152812 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( ( 1 + 438 T^{2} + 104849 T^{4} + 16454334 T^{6} + 1868658564 T^{8} + 154818828606 T^{10} + 9282206583569 T^{12} + 364841738158902 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 + 438 T^{2} + 104849 T^{4} + 16454334 T^{6} + 1868658564 T^{8} + 154818828606 T^{10} + 9282206583569 T^{12} + 364841738158902 T^{14} + 7837433594376961 T^{16} )^{2} \))
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