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Properties

Label 825.2.n
Level $825$
Weight $2$
Character orbit 825.n
Rep. character $\chi_{825}(301,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $152$
Newform subspaces $16$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 16 \)
Sturm bound: \(240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

Total New Old
Modular forms 528 152 376
Cusp forms 432 152 280
Eisenstein series 96 0 96

Trace form

\( 152 q - 4 q^{2} - 42 q^{4} + 2 q^{6} - 6 q^{7} + 8 q^{8} - 38 q^{9} + O(q^{10}) \) \( 152 q - 4 q^{2} - 42 q^{4} + 2 q^{6} - 6 q^{7} + 8 q^{8} - 38 q^{9} + 10 q^{11} + 8 q^{12} + 6 q^{13} - 6 q^{14} - 34 q^{16} + 2 q^{17} + 6 q^{18} + 20 q^{19} - 16 q^{21} + 36 q^{22} + 20 q^{23} + 24 q^{24} - 18 q^{26} - 16 q^{28} - 4 q^{29} - 8 q^{32} + 6 q^{33} - 40 q^{34} - 42 q^{36} + 46 q^{37} + 46 q^{38} + 16 q^{39} - 28 q^{41} - 22 q^{42} + 24 q^{43} + 70 q^{44} + 70 q^{46} + 18 q^{47} - 40 q^{48} - 76 q^{49} - 8 q^{51} - 62 q^{52} - 26 q^{53} - 8 q^{54} - 156 q^{56} - 8 q^{57} + 44 q^{58} - 14 q^{59} - 14 q^{61} + 12 q^{62} - 6 q^{63} - 118 q^{64} - 12 q^{66} + 12 q^{67} + 68 q^{68} - 2 q^{69} + 4 q^{71} - 2 q^{72} + 16 q^{73} + 50 q^{74} + 48 q^{76} + 94 q^{77} - 80 q^{78} + 34 q^{79} - 38 q^{81} + 50 q^{82} - 30 q^{83} + 72 q^{84} + 64 q^{87} + 42 q^{88} + 76 q^{89} + 26 q^{91} + 70 q^{92} - 52 q^{93} + 54 q^{94} + 20 q^{96} - 30 q^{97} - 136 q^{98} + 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
825.2.n.a \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(-3\) \(-1\) \(0\) \(-3\) \(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.b \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(-2\) \(1\) \(0\) \(8\) \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.c \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(0\) \(-1\) \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
825.2.n.d \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(2\) \(-1\) \(0\) \(-8\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.e \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(3\) \(1\) \(0\) \(3\) \(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.f \(4\) \(6.588\) \(\Q(\zeta_{10})\) None \(3\) \(1\) \(0\) \(3\) \(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.g \(8\) \(6.588\) 8.0.13140625.1 None \(-4\) \(2\) \(0\) \(-3\) \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
825.2.n.h \(8\) \(6.588\) 8.0.819390625.1 None \(-3\) \(2\) \(0\) \(-7\) \(q-\beta _{1}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.i \(8\) \(6.588\) 8.0.819390625.1 None \(-2\) \(-2\) \(0\) \(-9\) \(q-\beta _{4}q^{2}-\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
825.2.n.j \(8\) \(6.588\) \(\Q(\zeta_{15})\) None \(-2\) \(-2\) \(0\) \(5\) \(q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
825.2.n.k \(8\) \(6.588\) 8.0.13140625.1 None \(0\) \(2\) \(0\) \(-1\) \(q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(1+\cdots)q^{3}+\cdots\)
825.2.n.l \(8\) \(6.588\) 8.0.819390625.1 None \(3\) \(-2\) \(0\) \(7\) \(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{6})q^{3}+\cdots\)
825.2.n.m \(16\) \(6.588\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-4\) \(0\) \(4\) \(q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{6})q^{2}-\beta _{11}q^{3}+\cdots\)
825.2.n.n \(16\) \(6.588\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(2\) \(4\) \(0\) \(-4\) \(q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{6})q^{2}+\beta _{11}q^{3}+\cdots\)
825.2.n.o \(24\) \(6.588\) None \(-2\) \(6\) \(0\) \(-4\)
825.2.n.p \(24\) \(6.588\) None \(2\) \(-6\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)