Properties

Label 1400.2.g
Level $1400$
Weight $2$
Character orbit 1400.g
Rep. character $\chi_{1400}(449,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $11$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
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 264 28 236
Cusp forms 216 28 188
Eisenstein series 48 0 48

Trace form

\( 28q - 32q^{9} + O(q^{10}) \) \( 28q - 32q^{9} - 12q^{11} + 4q^{21} - 16q^{29} - 16q^{31} - 16q^{39} + 4q^{41} - 28q^{49} + 12q^{51} - 12q^{59} - 20q^{61} + 56q^{69} + 32q^{71} + 24q^{79} - 12q^{81} + 12q^{89} - 12q^{91} - 40q^{99} + O(q^{100}) \)

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.g.a \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+iq^{7}-6q^{9}-5q^{11}+5iq^{13}+\cdots\)
1400.2.g.b \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-iq^{7}-q^{9}+2iq^{17}+2q^{19}+\cdots\)
1400.2.g.c \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+iq^{7}-q^{9}+q^{11}+4iq^{13}+\cdots\)
1400.2.g.d \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-iq^{7}-q^{9}+5q^{11}-8iq^{17}+\cdots\)
1400.2.g.e \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}+2q^{9}-5q^{11}-iq^{13}+\cdots\)
1400.2.g.f \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}+2q^{9}-q^{11}-6iq^{13}+\cdots\)
1400.2.g.g \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+3q^{9}-4q^{11}+2iq^{13}+6iq^{17}+\cdots\)
1400.2.g.h \(2\) \(11.179\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+3q^{9}+q^{11}-2iq^{13}+4iq^{17}+\cdots\)
1400.2.g.i \(4\) \(11.179\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-6+\beta _{3})q^{9}+(3+\cdots)q^{11}+\cdots\)
1400.2.g.j \(4\) \(11.179\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
1400.2.g.k \(4\) \(11.179\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)