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Properties

Label 2100.2.s
Level $2100$
Weight $2$
Character orbit 2100.s
Rep. character $\chi_{2100}(1457,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $3$
Sturm bound $960$
Trace bound $1$

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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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(960\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

Total New Old
Modular forms 1032 72 960
Cusp forms 888 72 816
Eisenstein series 144 0 144

Trace form

\( 72 q + 4 q^{3} + O(q^{10}) \) \( 72 q + 4 q^{3} - 24 q^{13} - 8 q^{21} - 8 q^{27} + 32 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 16 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} + 144 q^{81} + 20 q^{87} + 48 q^{91} - 20 q^{93} + 104 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2100.2.s.a 2100.s 15.e $16$ $16.769$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{9}q^{3}-\beta _{14}q^{7}+(\beta _{7}+\beta _{11})q^{9}+\cdots\)
2100.2.s.b 2100.s 15.e $24$ $16.769$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
2100.2.s.c 2100.s 15.e $32$ $16.769$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)