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

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

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

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)