Properties

Label 1400.2.q
Level $1400$
Weight $2$
Character orbit 1400.q
Rep. character $\chi_{1400}(401,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $76$
Newform subspaces $15$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(480\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

Total New Old
Modular forms 528 76 452
Cusp forms 432 76 356
Eisenstein series 96 0 96

Trace form

\( 76q - 2q^{3} - 4q^{7} - 36q^{9} + O(q^{10}) \) \( 76q - 2q^{3} - 4q^{7} - 36q^{9} + 2q^{11} - 8q^{13} + 2q^{17} + 10q^{19} + 18q^{21} - 10q^{23} + 4q^{27} + 16q^{29} + 10q^{31} - 6q^{33} - 6q^{37} + 4q^{39} + 24q^{41} - 32q^{43} - 6q^{47} - 20q^{49} + 22q^{51} - 6q^{53} - 36q^{57} + 18q^{59} + 2q^{61} + 40q^{63} + 14q^{67} - 28q^{69} + 26q^{73} + 34q^{77} + 30q^{79} - 22q^{81} + 72q^{83} + 24q^{87} - 10q^{89} + 16q^{91} + 46q^{93} + 8q^{97} - 112q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1400.2.q.a \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-4\) \(q+(-2+2\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}+\cdots\)
1400.2.q.b \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(1\) \(q+(-2+2\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1400.2.q.c \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1400.2.q.d \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(4\) \(q+(-1+\zeta_{6})q^{3}+(1+2\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1400.2.q.e \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(5\) \(q+(1-\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
1400.2.q.f \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-1\) \(q+(2-2\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1400.2.q.g \(2\) \(11.179\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-4\) \(q+(3-3\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}-6\zeta_{6}q^{9}+\cdots\)
1400.2.q.h \(4\) \(11.179\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(0\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1400.2.q.i \(6\) \(11.179\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{3}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{3}+\cdots\)
1400.2.q.j \(6\) \(11.179\) 6.0.11337408.1 None \(0\) \(0\) \(0\) \(-6\) \(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1400.2.q.k \(6\) \(11.179\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(0\) \(q+(-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4})q^{3}+(2\zeta_{18}+\cdots)q^{7}+\cdots\)
1400.2.q.l \(8\) \(11.179\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(0\) \(3\) \(q+(\beta _{1}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\beta _{4})q^{7}+\cdots\)
1400.2.q.m \(8\) \(11.179\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(3\) \(0\) \(-3\) \(q+(-\beta _{1}-\beta _{5})q^{3}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
1400.2.q.n \(12\) \(11.179\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-1\) \(0\) \(-3\) \(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{4}q^{7}+(\beta _{6}-\beta _{10}+\cdots)q^{9}+\cdots\)
1400.2.q.o \(12\) \(11.179\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(1\) \(0\) \(3\) \(q+(-\beta _{1}-\beta _{3})q^{3}+\beta _{4}q^{7}+(\beta _{6}-\beta _{10}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)