Properties

Label 225.4.b
Level $225$
Weight $4$
Character orbit 225.b
Rep. character $\chi_{225}(199,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $9$
Sturm bound $120$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(120\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(225, [\chi])\).

Total New Old
Modular forms 102 24 78
Cusp forms 78 22 56
Eisenstein series 24 2 22

Trace form

\( 22q - 98q^{4} + O(q^{10}) \) \( 22q - 98q^{4} - 90q^{11} + 288q^{14} + 314q^{16} - 154q^{19} + 516q^{26} + 708q^{29} + 396q^{31} + 194q^{34} - 1326q^{41} + 402q^{44} - 324q^{46} - 1742q^{49} + 660q^{56} + 936q^{59} + 268q^{61} - 1066q^{64} - 2064q^{71} - 852q^{74} - 286q^{76} + 4860q^{79} + 4860q^{86} - 1206q^{89} - 1584q^{91} + 4160q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.4.b.a \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-17q^{4}+6iq^{7}-9iq^{8}-50q^{11}+\cdots\)
225.4.b.b \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-17q^{4}-6iq^{7}-9iq^{8}+50q^{11}+\cdots\)
225.4.b.c \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-8q^{4}+3iq^{7}-2^{5}q^{11}+\cdots\)
225.4.b.d \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{2}-q^{4}-20iq^{7}+21iq^{8}+\cdots\)
225.4.b.e \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+7q^{4}+24iq^{7}+15iq^{8}+\cdots\)
225.4.b.f \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+7q^{4}-6iq^{7}+15iq^{8}+43q^{11}+\cdots\)
225.4.b.g \(2\) \(13.275\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+8q^{4}+2iq^{7}+7iq^{13}+2^{6}q^{16}+\cdots\)
225.4.b.h \(4\) \(13.275\) \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{2}+(-12+2\beta _{2})q^{4}+\cdots\)
225.4.b.i \(4\) \(13.275\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-2q^{4}+3\beta _{1}q^{7}-6\beta _{2}q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)