Properties

Label 400.2.c
Level $400$
Weight $2$
Character orbit 400.c
Rep. character $\chi_{400}(49,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $120$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).

Total New Old
Modular forms 78 10 68
Cusp forms 42 8 34
Eisenstein series 36 2 34

Trace form

\( 8q - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{9} - 4q^{11} + 12q^{19} - 16q^{21} + 8q^{29} - 40q^{39} - 12q^{41} + 12q^{51} + 32q^{59} + 24q^{61} + 24q^{71} + 8q^{79} + 16q^{81} + 12q^{89} - 24q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
400.2.c.a \(2\) \(3.194\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+2iq^{7}-6q^{9}-q^{11}+4iq^{13}+\cdots\)
400.2.c.b \(2\) \(3.194\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3iq^{17}+\cdots\)
400.2.c.c \(2\) \(3.194\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-2iq^{7}+2q^{9}+3q^{11}+4iq^{13}+\cdots\)
400.2.c.d \(2\) \(3.194\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+3q^{9}-4q^{11}+iq^{13}+iq^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)