Properties

Label 2100.2.s
Level 2100
Weight 2
Character orbit s
Rep. character \(\chi_{2100}(1457,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 72
Newform subspaces 3
Sturm bound 960
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(960\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

Total New Old
Modular forms 1032 72 960
Cusp forms 888 72 816
Eisenstein series 144 0 144

Trace form

\( 72q + 4q^{3} + O(q^{10}) \) \( 72q + 4q^{3} - 24q^{13} - 8q^{21} - 8q^{27} + 32q^{31} + 20q^{33} - 32q^{37} + 8q^{43} + 16q^{51} + 28q^{57} - 8q^{63} + 24q^{67} + 144q^{81} + 20q^{87} + 48q^{91} - 20q^{93} + 104q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2100.2.s.a \(16\) \(16.769\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{3}-\beta _{14}q^{7}+(\beta _{7}+\beta _{11})q^{9}+\cdots\)
2100.2.s.b \(24\) \(16.769\) None \(0\) \(4\) \(0\) \(0\)
2100.2.s.c \(32\) \(16.769\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 - 23 T^{4} + 256 T^{8} - 1863 T^{12} + 6561 T^{16} \))
$5$ 1
$7$ (\( ( 1 + T^{4} )^{4} \))
$11$ (\( ( 1 - 29 T^{2} + 448 T^{4} - 3509 T^{6} + 14641 T^{8} )^{4} \))
$13$ (\( ( 1 + 17 T^{4} - 44912 T^{8} + 485537 T^{12} + 815730721 T^{16} )^{2} \))
$17$ (\( ( 1 - 1039 T^{4} + 433824 T^{8} - 86778319 T^{12} + 6975757441 T^{16} )^{2} \))
$19$ (\( ( 1 - 24 T^{2} + 254 T^{4} - 8664 T^{6} + 130321 T^{8} )^{4} \))
$23$ (\( ( 1 + 260 T^{4} + 141382 T^{8} + 72758660 T^{12} + 78310985281 T^{16} )^{2} \))
$29$ (\( ( 1 + T^{2} - 1416 T^{4} + 841 T^{6} + 707281 T^{8} )^{4} \))
$31$ (\( ( 1 - 6 T^{2} + 961 T^{4} )^{8} \))
$37$ (\( ( 1 + 932 T^{4} + 3112486 T^{8} + 1746718052 T^{12} + 3512479453921 T^{16} )^{2} \))
$41$ (\( ( 1 - 104 T^{2} + 5998 T^{4} - 174824 T^{6} + 2825761 T^{8} )^{4} \))
$43$ (\( ( 1 - 4828 T^{4} + 11812006 T^{8} - 16505971228 T^{12} + 11688200277601 T^{16} )^{2} \))
$47$ (\( ( 1 + 6137 T^{4} + 19047856 T^{8} + 29946602297 T^{12} + 23811286661761 T^{16} )^{2} \))
$53$ (\( ( 1 + 740 T^{4} - 5406938 T^{8} + 5838955940 T^{12} + 62259690411361 T^{16} )^{2} \))
$59$ (\( ( 1 + 6350 T^{4} + 12117361 T^{8} )^{4} \))
$61$ (\( ( 1 + 2 T + 106 T^{2} + 122 T^{3} + 3721 T^{4} )^{8} \))
$67$ (\( ( 1 - 2044 T^{4} - 20281946 T^{8} - 41188891324 T^{12} + 406067677556641 T^{16} )^{2} \))
$71$ (\( ( 1 - 84 T^{2} + 2054 T^{4} - 423444 T^{6} + 25411681 T^{8} )^{4} \))
$73$ (\( ( 1 - 96 T^{2} + 5329 T^{4} )^{4}( 1 + 96 T^{2} + 5329 T^{4} )^{4} \))
$79$ (\( ( 1 - 283 T^{2} + 32296 T^{4} - 1766203 T^{6} + 38950081 T^{8} )^{4} \))
$83$ (\( ( 1 + 8420 T^{4} + 39091942 T^{8} + 399599062820 T^{12} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( ( 1 + 116 T^{2} + 18118 T^{4} + 918836 T^{6} + 62742241 T^{8} )^{4} \))
$97$ (\( ( 1 + 32753 T^{4} + 439869408 T^{8} + 2899599540593 T^{12} + 7837433594376961 T^{16} )^{2} \))
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