Properties

Label 1400.2.bh
Level $1400$
Weight $2$
Character orbit 1400.bh
Rep. character $\chi_{1400}(249,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $10$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(480\)
Trace bound: \(11\)
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 72 456
Cusp forms 432 72 360
Eisenstein series 96 0 96

Trace form

\( 72q + 32q^{9} + O(q^{10}) \) \( 72q + 32q^{9} + 4q^{11} + 8q^{19} + 20q^{21} - 24q^{29} - 4q^{31} - 32q^{39} - 16q^{41} + 48q^{49} + 12q^{51} + 52q^{59} + 24q^{61} + 88q^{69} - 32q^{71} + 12q^{79} - 60q^{81} - 36q^{89} + 16q^{91} + 88q^{99} + O(q^{100}) \)

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.bh.a \(4\) \(11.179\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-2\zeta_{12}+3\zeta_{12}^{3})q^{7}+\cdots\)
1400.2.bh.b \(4\) \(11.179\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.c \(4\) \(11.179\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.d \(4\) \(11.179\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{3}+(3\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.e \(4\) \(11.179\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
1400.2.bh.f \(4\) \(11.179\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{12}q^{3}+(2\zeta_{12}+\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.g \(8\) \(11.179\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
1400.2.bh.h \(12\) \(11.179\) \(\Q(\zeta_{36})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{7}+\zeta_{36}^{11})q^{3}+\cdots\)
1400.2.bh.i \(12\) \(11.179\) 12.0.\(\cdots\).37 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{5}+\beta _{7}+\beta _{8})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1400.2.bh.j \(16\) \(11.179\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{9})q^{3}+(\beta _{6}-\beta _{7})q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)

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

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