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Properties

Label 2100.2.ce
Level $2100$
Weight $2$
Character orbit 2100.ce
Rep. character $\chi_{2100}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $96$
Newform subspaces $5$
Sturm bound $960$
Trace bound $21$

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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.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(960\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 2064 96 1968
Cusp forms 1776 96 1680
Eisenstein series 288 0 288

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 16 q^{11} - 4 q^{21} - 16 q^{23} - 48 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} + 16 q^{51} - 40 q^{53} + 16 q^{57} - 12 q^{61} + 12 q^{63} + 32 q^{71} + 60 q^{73} + 84 q^{77} + 48 q^{81} + 48 q^{87} + 20 q^{91} - 8 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2100.2.ce.a 2100.ce 35.k $8$ $16.769$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{24}^{3}-\zeta_{24}^{7})q^{3}+(-3\zeta_{24}^{3}+\zeta_{24}^{7})q^{7}+\cdots\)
2100.2.ce.b 2100.ce 35.k $8$ $16.769$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q-\zeta_{24}q^{3}+(-3\zeta_{24}+2\zeta_{24}^{5})q^{7}+\cdots\)
2100.2.ce.c 2100.ce 35.k $24$ $16.769$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
2100.2.ce.d 2100.ce 35.k $24$ $16.769$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
2100.2.ce.e 2100.ce 35.k $32$ $16.769$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)