Properties

Label 1200.2.v
Level $1200$
Weight $2$
Character orbit 1200.v
Rep. character $\chi_{1200}(257,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $13$
Sturm bound $480$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 13 \)
Sturm bound: \(480\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 552 76 476
Cusp forms 408 68 340
Eisenstein series 144 8 136

Trace form

\( 68 q - 2 q^{3} - 4 q^{7} + O(q^{10}) \) \( 68 q - 2 q^{3} - 4 q^{7} + 4 q^{13} + 12 q^{21} - 14 q^{27} + 24 q^{31} - 4 q^{33} + 20 q^{37} + 12 q^{43} + 52 q^{51} - 20 q^{57} + 24 q^{61} + 48 q^{63} + 20 q^{67} - 4 q^{73} - 20 q^{81} + 20 q^{87} + 32 q^{91} + 8 q^{93} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1200.2.v.a $4$ $9.582$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1200.2.v.b $4$ $9.582$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-4\) \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-1+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1200.2.v.c $4$ $9.582$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(12\) \(q+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+(3+3\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1200.2.v.d $4$ $9.582$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1200.2.v.e $4$ $9.582$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+2\beta _{1}q^{7}-3\beta _{2}q^{9}-4\beta _{3}q^{13}+\cdots\)
1200.2.v.f $4$ $9.582$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{1}q^{7}-3\beta _{2}q^{9}+3\beta _{3}q^{13}+\cdots\)
1200.2.v.g $4$ $9.582$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-3\beta _{2}q^{9}+4\beta _{1}q^{17}-4\beta _{2}q^{19}+\cdots\)
1200.2.v.h $4$ $9.582$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+3\beta _{1}q^{7}-3\beta _{2}q^{9}-\beta _{3}q^{13}+\cdots\)
1200.2.v.i $4$ $9.582$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(-4\) \(q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1200.2.v.j $4$ $9.582$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(-4\) \(q+(1-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{7}+\cdots\)
1200.2.v.k $4$ $9.582$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(8\) \(q+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)
1200.2.v.l $8$ $9.582$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{3}-2\zeta_{24}q^{7}+(2\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{9}+\cdots\)
1200.2.v.m $16$ $9.582$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)