Properties

Label 2100.2.bc
Level $2100$
Weight $2$
Character orbit 2100.bc
Rep. character $\chi_{2100}(949,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $8$
Sturm bound $960$
Trace bound $19$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(960\)
Trace bound: \(19\)
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 48 984
Cusp forms 888 48 840
Eisenstein series 144 0 144

Trace form

\( 48 q + 24 q^{9} + O(q^{10}) \) \( 48 q + 24 q^{9} + 12 q^{11} - 18 q^{19} - 2 q^{21} - 32 q^{29} - 16 q^{31} - 2 q^{39} - 72 q^{41} - 6 q^{49} - 8 q^{51} + 40 q^{59} + 46 q^{61} + 16 q^{69} + 80 q^{71} + 40 q^{79} - 24 q^{81} + 32 q^{89} + 2 q^{91} + 24 q^{99} + O(q^{100}) \)

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.bc.a 2100.bc 35.j $4$ $16.769$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}+(-3\zeta_{12}+\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.b 2100.bc 35.j $4$ $16.769$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.c 2100.bc 35.j $4$ $16.769$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{3}+(-\zeta_{12}+3\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2100.2.bc.d 2100.bc 35.j $4$ $16.769$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots\)
2100.2.bc.e 2100.bc 35.j $8$ $16.769$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{7}-\beta _{3}q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots\)
2100.2.bc.f 2100.bc 35.j $8$ $16.769$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}q^{3}+(-\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
2100.2.bc.g 2100.bc 35.j $8$ $16.769$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}q^{3}+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{6})q^{7}+\cdots\)
2100.2.bc.h 2100.bc 35.j $8$ $16.769$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}-\beta _{6}q^{7}-\beta _{3}q^{9}+(3+3\beta _{3}+\cdots)q^{11}+\cdots\)

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

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