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Properties

Label 2100.2.q
Level $2100$
Weight $2$
Character orbit 2100.q
Rep. character $\chi_{2100}(1201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $50$
Newform subspaces $13$
Sturm bound $960$
Trace bound $13$

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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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(960\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 1032 50 982
Cusp forms 888 50 838
Eisenstein series 144 0 144

Trace form

\( 50 q + q^{3} + q^{7} - 25 q^{9} + O(q^{10}) \) \( 50 q + q^{3} + q^{7} - 25 q^{9} + 2 q^{11} - 6 q^{13} + 3 q^{19} - 6 q^{21} + 8 q^{23} - 2 q^{27} + 8 q^{29} - 11 q^{31} + 6 q^{33} - 19 q^{37} - q^{39} - 12 q^{41} - 18 q^{43} + 14 q^{47} - 7 q^{49} - 12 q^{53} + 18 q^{57} - 12 q^{59} - 4 q^{61} + 7 q^{63} + 19 q^{67} + 32 q^{69} - 4 q^{71} + 15 q^{73} + 28 q^{77} - 13 q^{79} - 25 q^{81} + 52 q^{83} - 4 q^{87} - 32 q^{89} - 57 q^{91} - 5 q^{93} - 84 q^{97} - 4 q^{99} + O(q^{100}) \)

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.q.a 2100.q 7.c $2$ $16.769$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
2100.2.q.b 2100.q 7.c $2$ $16.769$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
2100.2.q.c 2100.q 7.c $2$ $16.769$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
2100.2.q.d 2100.q 7.c $2$ $16.769$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
2100.2.q.e 2100.q 7.c $2$ $16.769$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
2100.2.q.f 2100.q 7.c $4$ $16.769$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
2100.2.q.g 2100.q 7.c $4$ $16.769$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{3}-\beta _{1}q^{7}+\beta _{2}q^{9}+(3+\cdots)q^{11}+\cdots\)
2100.2.q.h 2100.q 7.c $4$ $16.769$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
2100.2.q.i 2100.q 7.c $4$ $16.769$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{3}+\beta _{1}q^{7}+\beta _{2}q^{9}+(3+\beta _{1}+\cdots)q^{11}+\cdots\)
2100.2.q.j 2100.q 7.c $4$ $16.769$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
2100.2.q.k 2100.q 7.c $4$ $16.769$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{1}q^{9}+\cdots\)
2100.2.q.l 2100.q 7.c $8$ $16.769$ 8.0.\(\cdots\).3 None \(0\) \(-4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(-\beta _{1}+\beta _{6})q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
2100.2.q.m 2100.q 7.c $8$ $16.769$ 8.0.\(\cdots\).3 None \(0\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{3}+(\beta _{1}-\beta _{6})q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)