Properties

Label 1975.1.d
Level $1975$
Weight $1$
Character orbit 1975.d
Rep. character $\chi_{1975}(1026,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $200$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1975 = 5^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1975.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 79 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1975, [\chi])\).

Total New Old
Modular forms 21 12 9
Cusp forms 15 9 6
Eisenstein series 6 3 3

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 9 0 0 0

Trace form

\( 9 q + q^{2} + 4 q^{4} + 2 q^{8} + 5 q^{9} + O(q^{10}) \) \( 9 q + q^{2} + 4 q^{4} + 2 q^{8} + 5 q^{9} - q^{11} + q^{13} + 7 q^{16} + q^{18} - q^{19} - 4 q^{21} - 3 q^{22} + q^{23} - 7 q^{26} - 5 q^{31} - 2 q^{32} + 8 q^{36} + 2 q^{38} - 3 q^{44} - 2 q^{46} + 5 q^{49} - 4 q^{51} + 3 q^{52} - 3 q^{62} + 2 q^{64} + q^{67} + 2 q^{72} + q^{73} - 8 q^{76} - q^{79} + 5 q^{81} - 4 q^{83} + 4 q^{84} - q^{88} - q^{89} - 2 q^{92} + q^{97} + q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1975, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1975.1.d.a 1975.d 79.b $1$ $0.986$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-395}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+q^{9}-2q^{11}+q^{16}+2q^{19}+\cdots\)
1975.1.d.b 1975.d 79.b $2$ $0.986$ \(\Q(\sqrt{-2}) \) $D_{4}$ \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}-q^{4}-\beta q^{7}-q^{9}+\beta q^{12}+\cdots\)
1975.1.d.c 1975.d 79.b $2$ $0.986$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-79}) \) None \(1\) \(0\) \(0\) \(0\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}+q^{8}+q^{9}+\cdots\)
1975.1.d.d 1975.d 79.b $4$ $0.986$ \(\Q(\zeta_{20})^+\) $D_{10}$ \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1975, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1975, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 3}\)